Answer:
There's 18.75 inches of space at each side of the picture.
Explanation:
We know that, the picture is 10.5 inches wide, and the wall is 4 feet wide.
First we have to transform feet to inches and subtract. So, we know that 1 feet is 12 inches, how much inches would be 4 feet?

So, the wall is 48 inches wide.
Now,

There's 37.5 inches of space. If the picture is in the middle, then each side would be have:

Therefore, there's 18.75 inches of space at each side of the picture.