Is there any additional information in the question? Does the question mention that the left limit exists? Or are you asked to show that both sides behave the same?
Assuming that the left limit exists, I wrote out the definition of the limit and got this. Given epsilon > 0, there is a d such that |x-0| < d => |f(x)-L|< e, where L is the assumed limit. Here I just make a change of variables x = y - a and then plug it in. That's equivalent to the right hand definition. I think it should be straight-forward to show that if the left side doesn't exist, then so does the right hand side.