The teacher said, "Let the boy go home now".

The teacher asked if the boy might be allowed to go home then.

The teacher said the boy might be allowed to go home then.

The teacher said that the boy may be allowed to go home now.

The teacher said that the boy might be allowed to go home then.

The teacher said that the boy might be allowed to go home then is the correct indirect speech conversion.

"Now" changes to "then" in reported speech, and "may" becomes "might" to maintain the past tense.