Ryan multiplied 2/7 times 3/7 and got 6/7 . What is the correct product?

To find the product of $\dfrac{2}{7}$ and $\dfrac{3}{7}$, we multiply their numerators and denominators. The numerator is $2\cdot3=6$, and the denominator is $7\cdot7=49$. So the correct product is $\boxed{\dfrac{6}{49}}$.

6/49