A rotary lawn sprinkler turns in an opposite direction to the direction of the streams of
water it emits.
What law of motion is this

Newton's third law of motion.

Explanation:

Water is ejected from the sprinkler because the sprinkler effectively exerts a force on it. Newton's third law states that if the sprinkler exerts a force on the water, the water must exert an equal force in the opposite direction on the sprinkler. Hence the sprinkler turns in the opposite direction to the water stream.