1. The problem states that $63 \times 76 = 4788$ and asks to find the number that fits in the gap in the equation: $$76 \times 63 = 63 + \boxed{\text{?}}$$ 2. We know multiplication is commutative, so: $$76 \times 63 = 63 \times 76 = 4788$$ 3. The equation given is: $$76 \times 63 = 63 + \boxed{\text{?}}$$ Substitute the known product: $$4788 = 63 + \boxed{\text{?}}$$ 4. To find the missing number, subtract 63 from both sides: $$\boxed{\text{?}} = 4788 - 63$$ 5. Calculate the subtraction: $$\boxed{\text{?}} = 4725$$ 6. Therefore, the number that goes in the gap is $4725$.