In the following question, the sentence given with blank to be filled in with an appropriate word. Select the correct alternative out of the four and indicate it by selecting the appropriate option.
My mother likes to _________ me by showing everyone my baby pictures.

The sentence refers to a common situation where parents make their children feel self-conscious or awkward in front of others in a playful or mildly uncomfortable way.
Embarrass means to cause someone to feel awkward, self-conscious, or ashamed, which perfectly fits the context of showing childhood baby pictures to others.

Stun means to shock or astonish.

Annoy means to irritate.

Shame means to humiliate severely for a wrongdoing, which is too harsh for this context.

Thus, embarrass is the most appropriate word.