if 2/3 of a lawn takes 3/4 of an hour, how much can I mow in one hour? Can you please explain how to do this problem?

Note that (3/4)(4/3) = 1

That is, 1 hour is 4/3 as long as 3/4 hour.

So, he can mow 4/3 as much: (2/3)(4/3) = 8/9 of the lawn.