There are two ways to read the numbers 4, 7, and 9 in Japanese?

Yes. The Japanese language does have two pronunciations for 4, 7, and 9.

The general difference:

4: し, よん

Because し is pronounced the same way as "death" in Japanese, it is usually pronounced よん or よ, except for the fixed expressions, such as April, Four Square, and so on.

7: しち, なな

7 is very difficult to distinguish, and the two are used interchangeably. It can only be understood through accumulation

9: く, きゅう

9 is almost the same as 4, and く is pronounced the same way as 苦, so it's usually pronounced きゅう, except for fixed sayings: e.g. September, etc.

Expanded Information

Japanese Numbers 1~15:

1: いち

2: に

3: さん

4: よん/shi

5: ご

6: ろく

7: なな/shichi

8: はち

9: きゅう/く

10: じゅう

11: じゅういち

12: じゅうに

13: じゅうさん

14: じゅうよん

15: じゅうご