1. The problem is to find the product of $2y^2$ and $y^2$. 2. The formula for multiplying powers with the same base is $a^m \times a^n = a^{m+n}$. 3. Applying this rule, multiply the coefficients and add the exponents of $y$: $$2y^2 \times y^2 = 2 \times y^{2+2} = 2y^4$$ 4. So, the product of $2y^2$ and $y^2$ is $2y^4$.