1. **Problem Statement:** Calculate the product of the two-digit numbers $64$ and $63$. 2. **Formula:** Multiplication of two numbers $a$ and $b$ is given by $$a \times b$$. 3. **Step-by-step calculation:** - Multiply the units digit of the second number by the first number: $$64 \times 3 = 192$$ - Multiply the tens digit of the second number by the first number and shift one place to the left (multiply by 10): $$64 \times 6 = 384$$ $$384 \times 10 = 3840$$ - Add the two results: $$192 + 3840 = 4032$$ 4. **Final answer:** $$64 \times 63 = 4032$$ This method uses the distributive property of multiplication over addition: $$a \times (b+c) = a \times b + a \times c$$. The product of $64$ and $63$ is $4032$.