According to the Remainder Theorem, we can predict the remainder of dividing f(x) by x+4, by substituting x=-4 into f(x): 2*(-64)-3*16-45*(-4)-54=-128-48+180-54=180-230=-50. The synthetic division is used to check that the real remainder is -50. The question marks on the middle line are: -8 44 4 and on the bottom line: -11 -1 -50. The last figure is the true remainder, so the theorem is correct.
Let's see where the figures come from. Multiply 2 on the bottom line by -4 to give us -8 as the first figure on the middle line. Add -8 to the figure above it, -3, to give -11 on the bottom line. Multiply -11 by -4 to give us 44 on the middle line, then add it to -45 to give us -1 on the bottom line. Finally, multiply -1 by -4 to give us 4, which is the last figure on the middle line, and add it to -54 to give us the remainder -50 on the bottom line.