“möchten” = "would like" is not an infinitive but the conditional form of the verb "mögen". It is normally used with another verb in the infinitive which goes to the end of the clause, e.g.

Wir möchten Fußball spielen. (We would like to play soccer.)

Ich möchte im Sommer nach Deutschland fahren. (I'd like to go to Germany in the summer.)

Sometimes this other verb can be dropped if the meaning is already clear from the context, e.g.

Möchtest du eine Tasse Kaffee [haben]? (Would you like [to have] a cup of coffee?)

the verb-endings of "möchten" (Pay special attention to the third person singular):