The answer depends on how fussy you need / want to be about fractional
months. A person's exact age in terms of years is easy enough; months
are trickier because they are not the same number of days.

Here is a simplified way to do it, with the birthdate in A1 and the
given date in B1. Assume a month is 365 / 12 days. The Years
calculation is
=INT((B1-A1)/(365/12)/12)

The months calculation is
=MOD((B1-A1)/(365/12),12)

If you try this you'll likely get a result with decimal places in the
months response, so you may want to apply a rounding protocol or at
least be prepared to explain what the fractions truly mean.