The analogy compares CUP to LIP, so first let's work out what category of word LIP belongs to, then test each option against that category for BIRD.
Sorting the options by category immediately narrows it to the one body-part word, BEAK, which also matches the meaning of the analogy: just as a cup's lip is the part through which liquid passes, a bird's beak is the part through which it takes in food.
Therefore, the correct answer is BEAK.