In German, the endings of verbs change depending on the person you're talking about. Some remnants of this can still be seen in English: you say "I like" but "he like-s" with an additional "s".

The forms of "mögen" (to like) are:

ich mag (I like)

du mag-st (you [singular, familiar] like)

er/sie/es mag (he/she/it likes)

wir mög-en (we like)

ihr mög-t (you [plural, familiar] like)

sie/Sie mög-en (they/you [singular & plural, formal] like)

In your sentence, you're talking about "er" (he), so you have to choose "mag".

Unfortunately, like all the other modal verbs (e.g. can, must, may), "mögen" does not behave like a normal, regular verb. There is a vowel change in the entire singular (ö->a) and there are no verb endings for "ich" and "er/sie/es". A normal, regular verb looks like this in the present tense:

mach-en (to make, to do)

ich mach-e

du mach-st

er/sie/es mach-t

wir mach-en

ihr mach-t

sie/Sie mach-en