It is wrong.
He could not only understand it but also I could review the problem again.
When you use "not only... but also..." it is like you are making two 'branches' of the same sentence. What appears after "not only" and after "but also" should be able to make a complete sentence with what went before, for example:
I ate not only my sandwich but also my fries.
- I ate my sandwich
- I ate my fries
The problem with your sentence is that the first part is about someone else, but the second part about you. You are in effect saying:
- He could understand it.
- He could I could review the problem again <-- ungrammatical
You should instead say either:
Not only could he understand it, but also I could review the problem again.
Or, a much simpler way to express this would be:
He could understand it, and I could review the problem again.