"With pleasure" and "My pleasure"

If someone asked me to help, and I was willing to help them, I would say 'With pleasure', meaning that I would be pleased to help.

If we're talking of the situation, not the exam question, I would, in truth, say neither. "With pleasure" is a bit excessive. I think "no problem" coupled with movement to assist is sufficient.

If they said 'Thank you' after I had helped them, I might say 'My pleasure'. That is a shortened form of 'It was my pleasure', meaning I enjoyed helping you.
'My pleasure' means approximately the same thing as 'You're welcome', though it is slightly more formal.

IF I wished to be wordy and engage the beautiful woman, "I'd be pleased to help you." This is, in effect, the low-register version, of "It would be my pleasure to help you."