Two Directions

Both parts of $47\cdot 6+53\cdot 6$ are multiplied by 6. So write the 6 once, in front of a bracket:

$$6\cdot \left(47+53\right) = 6\cdot 100 = 600$$

This is called factoring. It is the opposite of expanding. Expanding turns $4\left(x+5\right)$ into $4x+20$. Factoring turns $4x+20$ back into $4\left(x+5\right)$.