Because the English sentence doesn't use a definite article either ("families", not "the families"). And it's "mögen", not "mogen".

Its plural restaurants, so mogen (Ich mag, Wir mogen)

"Mochte" is past tense ("liked") and used with the 1st person singular (="I") or the 3rd person singular (="he/she/it"). E.g. Der Mann mochte das Restaurant. = The man liked the restaurant.

(In case you meant "möchte" -- that means "would like" for the 1st person singular and the 3rd person singular, i.e. it's not the right word here either.)

In the sentence in the exercise, you need the present tense of "like" and the form for the 3rd person plural ("they") = "mögen".