I received stocks from a spin-off of a firm from which I possess some stocks. Which date is used to determine if capital gains are short or long-term?

From IRS Publication 550, page 53:

Stock dividends

The holding period for stock you received as a taxable stock dividend begins on the date of distribution.

The holding period for new stock you received as a nontaxable stock dividend begins on the same day as the holding period of the old stock. This rule also applies to stock acquired in a spin-off, which is a distribution of stock or securities in a controlled corporation.

Specifically from the INFORMATION STATEMENT TO PFIZER STOCKHOLDERS

the holding period (for tax purposes) of any shares of Newco [Upjohn Inc.] common stock received (including any fractional shares of Newco common stock deemed received and exchanged for cash, as described below) by a U.S. Holder or Non-U.S. Holders of Pfizer common stock will include such holder’s holding period in such Pfizer common stock at the time of the Distribution.

Pfizer will spin-off its Upjohn subsidiary, calling it Newco. Next, Newco and Mylan will merge. Newco will be renamed “Viatris” (ticker symbol “VTRS”) and will operate both Mylan and Upjohn. This type of M&A transaction is called a Reverse Morris Trust. There are two stages, occurring on the same or subsequent days. The Distribution is first, followed by the Combination.

Via EX-99.1 Pfizer, Newco, Mylan: Explanatory Note:

Distribution: Pfizer will distribute all shares of Newco by means of a spin-off. Newco common stock will be distributed on a pro rata basis to Pfizer stockholders as of the record date of the Distribution.

Immediately following the Distribution, Newco and Mylan will engage in a Combination transaction in which Mylan shareholders will receive shares of Newco common stock.

Which date is used to determine whether capital gains are short-term or long-term?

Via EX-99.1 Pfizer, Newco, Mylan: Material U.S. Federal Income Tax Consequences:

The holding period (for tax purposes) of any shares of Newco common stock received (including any fractional shares of Newco common stock deemed received and exchanged for cash...) by a U.S. Holder of Pfizer common stock will include such holder’s holding period in such Pfizer common stock at the time of the Distribution.

Capital gains (of non-corporate U.S. Holders, including individuals) will be eligible for the preferential U.S. federal income tax rates applicable to long-term capital gains if the U.S. Holder has held its Pfizer common stock for more than one year as of the closing date of the Combination.