context free – Does this grammar accept this words?

It looks the grammar indeed accepts all words of the form $(b+a)^nca^n$ (which means, all words that start with any sequence of $n$ $b$‘s and $a$‘s, and then a single $c$ and afterwards exactly $n$ times the letter $a$).

To show why, try to show the two following things:

  1. every word accepted by the grammar must be with such form

  2. every word with such form has a derivation sequence in the grammar.

The first statement can be easily proved by induction (over sequence derivation length), if you notice that each derivation of $S$ adds only one element to both sides.

The second statement can be much more easily proved, try to think of what derications are necessary to create such words.