Cancel First

$\frac{4}{15}\cdot \frac{5}{6}$ multiplies to $\frac{4\cdot 5}{15\cdot 6}$, which is $\frac{20}{90}$, and then you still have to simplify it. There is a shorter road: simplify before you multiply.

Every top ends up on the top of the product and every bottom on the bottom, so any top can be simplified with any bottom, even the other fraction's. 4 and 6 share a 2: they become 2 and 3. 5 and 15 share a 5: they become 1 and 3. The product is now $\frac{2}{3}\cdot \frac{1}{3}$, which is $\frac{2}{9}$.

This is called cancelling. It is the same division by a shared factor that simplifying does, done while the numbers are still small. If you cancel every shared factor first, the product comes out in lowest terms. Two tops can never cancel with each other, though: dividing two tops changes the value.