Hiii

So here is the answer to the question

A/c =  A/b * B/c
      =3/4  *  8/9
      = 2/3

So a:c = 2:3

If you do not understand how it is done above i am providing another solution also.

a/b = 3/4,
so,    4a =  3b  (by transposition)..........eq 1
  
b/c =  8/9,
So,     8c = 9b
  also,   b= 8c/9  ...... eq 2

Putting eq 2 into eq 1

4a = 3 ( 8c/9)
when you solve this, you will get
4a = 8c / 3
transpose 3 to the other side
4*3(a)  = 8c
12a = 8c
so,
a/c = 8/12 = 2/3

Hence,
a:c = 2:3

Hope it helps.

Thanks!