1. **State the problem:** We need to find the product of $4X^2$ and $3X^2$. 2. **Formula used:** When multiplying terms with the same base, multiply the coefficients and add the exponents: $$aX^m \times bX^n = (a \times b)X^{m+n}$$ 3. **Apply the formula:** Here, $a=4$, $b=3$, $m=2$, and $n=2$. 4. Multiply the coefficients: $$4 \times 3 = 12$$ 5. Add the exponents of $X$: $$2 + 2 = 4$$ 6. **Final expression:** $$12X^4$$ 7. **Answer:** The product of $4X^2$ and $3X^2$ is $12X^4$.