Context-free grammar for $\{ a^n b^m a^{n+m} \}$
First, rewrite $a^nb^ma^{n+m}$ as $a^nb^ma^ma^n$. Now, from the outside in, you need rules to (1) add an $a$ to the front and back of your strings, and (2) to add $b$ to the front and $a$ to the back. It's also helpful to imagine building strings from the inside out... you can either add a $b$ to the front and an $a$ to the back, or an $a$ to both ends.

The first, working from the outside, rule is straightforward: 

S := aSa


Notice that once you start adding $b$, you cannot go back to adding only $a$... so we need a new nonterminal:

S := B
B := bBa


Since the empty string is in your language, add another production to allow $B$ to generate the empty string. So we get:

S := aSa | B
B := bBa | -