This is simply using the high-low method from Paper F2 (and you can find lectures on it in the lectures that go with chapter 17 of the Paper F2 free lecture notes).
The variable cost = (21200 – 15600) / (100 – 65) = $160 per unit.
Substituting for 100 units, the total cost is 21,200. The variable cost is 100 x 160 = 16000 Therefore the fixed cost is 21200 – 16000 = $5,200