Every odd number can be written in a form 2k +1, where k is integer.

let the four consecutive odd numbers be

2k - 1, 2k + 1, 2k + 3, 2k + 5, where k is integer

the product of the first and third will be 64 less than the product of the 2nd and 4th

(2k - 1)(2k + 3) = (2k + 1)(2k + 5) - 64

multiply and simplify we find

4k - 3 = 12 k - 59

8k = 56

k = 7

2k - 1 = 13

2k + 1 = 15

2k + 3 = 17

2k + 5 = 19

the four consecutive odd numbers are 13, 15, 17 and 19.