This might be easier to understand:
Get b to the same value in each ratio.
Easiest way to do this is do b in the first ratio multiplied by b in the second ratio = 3 x 4 = 12. Now change each ratio appropriately.
a:b = 2:3 = 8:12 <--- x4 to each part of ratio.
b:c = 4:5 = 12:15...