Context free grammar construction My problem with CFG is, I am to generally create ones that don't have requirements such as:

$\qquad \{a^m b^n \mid m \le n \le 2m \}$

I have no clue where to begin, and how to approach it. I was wondering if you can provide some hints for such daunting problems, along with how to solve that problem.

This is not homework, this is merely me trying to learn it. I solved many problems that did not have such requirements, but those problem are the ones where I am forced to look at the solution.
Just read the constraint carefully. $m\le n$ tells you that you must have at least as many b's as a's. The other part: $n\le 2m$ tells you that you cannot have more than twice as much a's.

Here is an EBNF description that yon can convert to BNF.

$S\to aSb[b] \mid \epsilon$