Is it obligatory to make up the remaining four rak'ahs of Duha prayer after forgetting them and remembering them after Asr?

The Duha prayer is a confirmed Sunnah. Its minimum is two rak'ahs, and its most complete form is eight rak'ahs. You are not required to make up the four rak'ahs you intended to pray, because you performed what is sufficient, and there is no harm in what you did.