To answer this question, we have that:
1. Mr. Thompson drove 75 miles in May.
2. He drove 6 times as many miles in July as he did in May. Then, he drove 6 * 75 miles = 450 miles in July.
3. He drove 4 times as many miles in June as he did in July.
Then, we have that Mr. Thompson drove in July 450 miles. If he drove 4 times miles in June as he did in July, we have that he drove:
450 miles * 4 = 1800 miles.
Therefore, he drove 1800 miles in June.