Step 1 :Let b represent the initial number of boxes. After buying 8 more boxes, Mark had (b + 8) boxes. Half of these boxes were destroyed in the fire, so the remaining boxes can be represented as \(\frac{b + 8}{2}\). We know that this is equal to 20 boxes. So, our equation is: \(\frac{b + 8}{2} = 20\)
Step 2 :To solve the equation, multiply both sides by 2: \(b + 8 = 40\). Then, subtract 8 from both sides: \(b = 32\). \(\boxed{32}\) is the initial number of boxes Mark had.