Ping lives at the corner of 3rd street and 6th avenue. ari lives at the corner of 21st street and 18th avenue. there is a gym the distance from ping's home to ari's home. where is the gym? 9th street and 10th avenue 12th street and 12th avenue 14th street and 12th avenue 15th street and 14th avenue

We need to determine the location of the gym considering that is located in the same distance with Ping and Ari's place. Such as to solve this, we have the solution below:
Ping place is 3rd street and 6th avenue which is (3,6)
Ari's place is 21's street and 18th avenue which is (21,18)
Solving the distance which is half way, we have
street midpoint = (3+ 21) / 2 = 12 streets
avenue midpoint = (6+18) / 2 = 12 avenue

The answer is 12th street and 12th avenue.