Designing CFG that accepts a^n b^m (n<m<2n)
Try this to remove the two cases the first time :

$$S\to aAb$$
$$A\to aCbb$$
$$C\to aCb|aCbb|\lambda$$

If you go to $A$ you cannot have $a^nb^{2n}$ and while going from $A$ to $aCbb$ you are removing the possiblity to get $a^nb^n$.