Change the narration: He said, "Let me do what I like".

He said that he might do what he liked.

He told that he can do what he likes.

He suggested that he might be allowed to do what he liked.

None of these

He suggested that he might be allowed to do what he liked.

"Let me do..." in indirect speech is often changed to "he might be allowed to...".

The reporting verb "said" can be expressed as "suggested" to convey a polite request or desire.