Your teacher is right. There is no reason to use algebra, which is misused in many problems as a shortcut, and slows the actual learning of math skills.
Here, the solution is as follows:
1. Find the volume of water in tank X.
2. Find the TOTAL base area of the three tanks, imagine that you have a larger tank with the same base area as the sum of the three.
3. Find the height of water in the new tank.
1. Find the volume of water in tank X.
Volume = 32*20*39.5=25280 cm^3
2. Find the TOTAL base area of the three tanks, imagine that you have a larger tank with the same base area as the sum of the three.
Total base area = 32*20 + 30*16 + 20*8 = 640+480+160 = 1280 cm^2
3. Find the height of water in the new tank
Height = Volume / base area
= 25280 / 1280
= 19.75 cm