To solve this question, the user needs to know the meaning of the phrase "egg on his face," which means to be embarrassed or humiliated by something that you have done.

Now, let's go through each option and explain why it is right or wrong:

A. on his teeth: This option is incorrect because having egg on your teeth is not an idiom that conveys embarrassment or humiliation.

B. on his face: This option is correct. When someone has "egg on their face," it means they are embarrassed or humiliated by something they have done or failed to do. In this case, Jack is embarrassed because he couldn't remember how to spell "Batman."

C. on his shirt: This option is incorrect because having egg on your shirt is not an idiom that conveys embarrassment or humiliation.

D. on his fingers: This option is incorrect because having egg on your fingers is not an idiom that conveys embarrassment or humiliation.

Therefore, the answer is: B. on his face.