I have a custom baby gate that has two swinging doors that open either way. How do I make them swing closed when opened from either direction!

Use double-acting spring hinges, also known as bi-swing spring hinges or double-action spring hinges.

A vendor lists some additional names:

Saloon Door hinges, Cafe Door hinges, Swinging Door Hinges, or Double Acting Barrel Hinges.

The design of the door would be helpful for illustrative purposes, but I think that you could probably make it work with a stiff spring.

Since this is a DIY forum, see the DIY idea below.

The idea is not to stretch the spring outward but side to side- allowing the straightening force to close the door. You may also need some medium washers to secure the spring. You can probably cover the spring with a hose or a fabric tube so that baby doesn't get pinched.