What is the following difference? 11√45 - 4√5 (picture attached)

The answer is 29√5. 

Since 11√45 and 4√5 do not share a common radical, you cannot subtract them. By looking at the equation, you can see that 11√45 is not fully simplified yet by the 45 within the square root.
Breaking it up into squares, you can find that 3 x 3 x 5 = 45, which can be translated into 3² x 5. Since the 3 is a square component in the 45, you can now extract it. Extract the 3 by dividing it from the 45 within the square root and multiplying it into the 11.
Your result is a 33√5, which shares a common radical with 4√5. You can now subtract 33√5 and 4√5, which is 29√5.

Side note: I noticed you got the answer wrong because you chose 7√40. I presume it's because you subtracted the components individually. I suggest that you look up lessons about simplifying radicals, along with adding and subtracting them. Hope this helps!