Yup. Your "explanations to make" makes sense. But (as you made clear up front) it's awkward. So I agree that it would be a disservice to encourage a student to use it.
I don't find it awkward, and it is used. I see no reason to discourage students from using it in the right context. The context I had in mind (
Why are you typing another post? Oh, let me guess. You've got some explanation to make) was one in which
make relates to
write or
type (an explanation to write) or
compose (an explanation to compose). The idea is that something is being created (a post with an explanation) which didn't already exist.
We can give explanations, provide explanations, offer explanations, make explanations, write explanations, compose explanations, type explanations, etc.
I'd like to apologize to tedmc, who, in Post #4, which the moderators seem to have overlooked in their "likes," made the same important point I was making in Post #14, his unfortunate mistake (analogous to my choosing the unpopular verb "make") being simply to leave "You got" unedited. What he pointed out, regardless, was that the second construction in the OP is possible with that little shift of "do" to a different verb.