Oliver runs a mile in 6 minutes. He runs 2 miles North and 3 miles east, so the total distance he ran is 2 + 3 = 5 miles.
Since he ran the same distance back to his house, the total distance he ran is 52 = 10 miles.
Since he runs a mile in 6 minutes, the total time of Oliver's run was 106 = 60 minutes.
Therefore, Oliver's total run time is 60 minutes.