____,he often helps me with my study

可以,但句型不一样了：
He is busy.However,he often helps me with my study.
== Busy as he is,he often helps me with my study.
== He is busy.He often helps me with my study,though / however.
== However busy he is,he often helps me with my study.
=== Despite the fact that he is very busy,he often helps me with my study.

应选D no matter how busy he is. no matter how 是一个词组 表示不论的意思 它后面的句子不用倒装。

No matter how busy he is,he often helps me with my study.
不管他有多忙，他都常常帮助我学习。

However busy he is=how busy he is, 不需要倒装；no matter how 后边不需要倒装