Can those happy moments be ever forgotten by me?

The correct answer is: B. Can I ever forget those happy moments?

The other options are:

• A. Shall I ever forget those happy moments? This is a question of obligation, not possibility. It is asking whether or not I am required to forget those happy moments. The answer is no, I am not required to forget them.
• C. Will I ever forget those happy moments? This is a question of prediction, not possibility. It is asking whether or not I am likely to forget those happy moments. The answer is I cannot say for sure whether or not I will forget them.
• D. Could I ever forget those happy moments? This is a question of possibility, but it is framed in a way that suggests that it is unlikely that I will forget those happy moments. The answer is yes, I could forget those happy moments, but it is unlikely that I will.

The reason why the correct answer is B. Can I ever forget those happy moments? is because it is the only option that is framed in a way that allows for the possibility of forgetting those happy moments. The other options all suggest that it is unlikely or impossible that I will forget those happy moments.