To solve this, first we calculate the exponents:

(2/5)^2 = (2^2)/(5^2) = 4/25
(1/3)^2 = (1^2)/(3^2) = 1/9

Now, substitute these values back into the expression:

15(4/25) - 63(1/9)

Now simplify the multiplication:

= 15(4/25) - 63(1/9)
= 60/25 - 63/9
= 12/5 - 63/9

Now, find a common denominator to subtract the fractions:

= (129)/(59) - (635)/(95)
= 108/45 - 315/45

Now, subtract the fractions:

= (108 - 315)/45
= -207/45
= -46

Therefore, 15(2/5)^2 - 63(1/3)^2 equals -46.