You should have mentioned the question in the message box.
Anyways, when two ratios of three different variables are given and both the ratios have one of the given three variables in common, then make that common variable equal in both the ratios.

Consider the present question

here a:b = 5:4 and b:c=9:8, so we should try to make the value of b equal in both the ratios.

the best way to do this is to take the LCM (Least common multiple) of both the numbers .

here the LCM will be 4*9 = 36

So a:b=5*9:4*9 = 45:36 and b:c= 9*4:8*4 = 36:32

Hence the combined ratio of all three variables ac = 45:36:32

Chinn_asama wrote:
4a=5b and 8b=9c, find ac

can anyone explain how to find the c value?

Thanx

To make the math easy, let b = the product of the coefficients of a and c:
b = 4*9 = 36.

Plugging b=4*9 into the two equations, we get:
4a = 5(4*9)
a = 45.
8(4*9) = 9c
c = 32.

Thus, ac = 45:36:32.