Learn Finnish: Kaksi munkkia kieltäytyy viinistä ja lihasta.

This is the required verb rection for kieltäytyä (to refuse, to decline). It always forces the thing being refused into the elative case (-sta / -stä). You can conceptualize it as pulling yourself "out of" an offering.

Why is the verb kieltäytyy in the singular if the subject is "two monks"?

When a sentence subject starts with a number other than yksi, the noun is put into the partitive singular (here, munkkia). In these cases, Finnish treats the number itself as a singular grammatical subject, so the verb must take the third-person singular form rather than the plural.

How does kieltäytyä relate to the base verb kieltää?

Kieltää means "to forbid" or "to deny" someone else. The suffix -ytyä in kieltäytyä makes it an automative or reflexive verb. By refusing an offer, you are essentially forbidding yourself from taking it.

How would you say "Two monks refuse to drink wine" using this same verb?

Since kieltäytyä always requires the elative case, you must put the verb "to drink" into its third infinitive elative form (-masta / -mästä). The sentence would be: Kaksi munkkia kieltäytyy juomasta viiniä.