Can two 120V outlets be converted to one 240V for stacked washer dryer combo?

Probably not, the amperage required by a modern dryer is larger than is available from a standard 120V outlet.

You'll probably need an electrician to run a properly sized new cable from the electric service to the unit location.

The premise seems a bit odd: an all electric townhouse that, apparently, didn't have an electric dryer before. All the dryers I know knew of in 120/240 land, whether standalone or 24" stacked, require 240V. For a long time, that was the standard. But, as noted by others, there are now a number of dryers or combination washer/dryers that will run on just 120V! The times they are a changin'.

That being said, let's assume for the moment that you indeed do not have a 240V receptacle (typically NEMA 14-30) available in the laundry room.

Combine Receptacles

This is technically sometimes possible. Specifically, if you have 2 120V receptacles on different legs, then this can be done technically. If the receptacles are side-by-side (e.g., a duplex receptacle or two receptacles next to each other) then you can test this with a multimeter. You will either get 240V between the hot pins or 0V. If it is 240V, then the following issues apply:

• Must be a Pair

Code requires that to combine two 120V circuits on opposite poles into one 240V circuit, the breakers must be next to each other (sort-of - could be outer pair of a proper quadplex, but that is actually one big unit that covers 2 full spaces, so depends on how you define "next to each other") and have common maintenance shutoff. As you will find in many questions & answers here, that can mean a handle-tie (so that the breakers trip independently but are manually shut off together) but normally just means a double breaker.

• Must have Appropriate Wire

Typical 120V receptacles use 14 AWG wire on a 15A breaker or 12 AWG wire on a 20A breaker. But for a dryer, you typically need 10 AWG wire on a 30A breaker. If you need to replace the wire and the receptacle, you might as well run a new circuit. I find it highly unlikely that you will find 10 AWG wire on a 15A or 20A circuit, at least in an ordinary house.

• You must have a 120V receptacle for the laundry room

AFAIK, you must have a 120V receptacle in the laundry room. If you convert these 2 receptacles to 240V, and you don't have any other receptacles in the room, then you can't do this. You can't just use the same circuit for 120V and 240V because of the 30A (dryer) vs. 20A (regular receptacles) problem - the 30A breaker would not properly protect appliances plugged into the 120V receptacle.

So all of that points to being able to legally combine the 2 120V circuits to get 1 240V circuit being extremely unlikely.

New Circuit

The usual solution is a new circuit. How easy/hard that will be depends on the distance (and obstacles) between the breaker panel and the laundry room, and how full your breaker panel is.

But check carefully to make sure there isn't another circuit lurking somewhere nearby. I find it unlikely (but not impossible) that an all electric townhouse built in 1982 would not have a 240V circuit for a dryer, unless it was split into 2 120V circuits for use elsewhere, which is possible. 240V -> 120V is much easier than the other way around - you can always use 10 AWG where you only need 12 AWG.

Your unit already has a 240V dryer plug. Guaranteed.

An all-electric townhouse built in 1982 WILL have a 240V electric dryer plug in the laundry room. Period, fullstop, end of subject. You just haven't found it yet.

While you're searching, also search for a gas line. That would be very surprising in a development that is all electric, because usually the whole point of going all-electric in a condo complex is to avoid even having to bring gas onto the property! For instance my friend has an all-electric house, the entire square mile does not have gas lines.

I suspect you'll find no gas line. If so, it is impossible for the building to receive an occupancy permit without a 240V dryer socket in the laundry area. It MUST be there.

The longshot

Which makes no sense, because if the last guy did this, there'd be no way to dry clothes!!!!

Now, you know what the common 120V dual receptacle looks like. Maybe you've also seen "single" 120V receptacles with a round socket instead of oval. Each of those fits in a space we call a "gang" (no idea why).

If you're seeing two of those next to each other (say, 4 sockets, or 2 singles next to each other, or a duplex and a single) in a "2-gang" space with a basically square cover plate... then it's remotely possible that somebody hijacked the 240V dryer plug and replaced it with dual 120V circuits.

The hint is that a 240V dryer socket normally takes a 2-gang space.

Conversion in that direction is possible (240 to dual 120s). And if that "240 -> dual-120" conversion was done, it can be un-done.

Other than that, conversion in the other direction is not possible: you can't take any random pair of 120V circuits and turn them into a 240V circuit.

This all seems highly improbable... but as Sherlock Holmes says, when you eliminate the impossible (the townhouse not having any dryer power), what remains no matter how improbable must be the truth.

Heat pump dryers to the rescue!

While traditional and even condensing electric dryers indeed draw far too much power to run on a 120V laundry circuit, thanks to the marvel of modern technology known as a heat pump dryer, all hope is not lost in your situation! In particular, the Miele TWB1xx series of dryers plug into a standard 120V circuit and draws about 1kW of power; this permits it to be stacked with one of the Miele compact front loading washers using the manufacturer's WTV502 stack kit, while sharing the laundry branch circuit with the washer. This does pull about 2.3kW of power from a 120V/20A circuit, but since you aren't expected to be running your washer and dryer for several hours straight on a regular basis, this is acceptable.

Note that while you won't need a dryer vent for the dryer I recommend, you'll need to rig the drain hose since heat pump dryers discharge the moisture from the clothes as condensate. (They are basically dehumidifiers for clothes.) Also, this trick only works with the Miele dryers; heat-pump dryers from other manufacturers are either 240V-only (Blomberg/Beko) or 120/240V (Samsung).