what would be the height of the tank if it is 50cm wide and 60cm long and it can hold up to 126 liters of water but they recommended filling

There is a problem here xerxes.   

1cm^3 hold 1ml

so there are 1000cm^3 in a litre

I am ashamed  It is probably getting too late for me. 

I thought about 1dm^3 being 1litre. But that's alright. 

$$1dm^3 = 1litre$$

If the pool would be 10cm high, we would have 30dm^3 of content. We are now looking for a height. 10cm of height means we have 30 litre of content.  

Hence that:

$${\frac{{\mathtt{126}}}{{\mathtt{30}}}} = {\frac{{\mathtt{21}}}{{\mathtt{5}}}} = {\mathtt{4.2}}$$

As we calculate in dm:

42cm

and if we just fill the pool by 2/3s:

the height should be 63cm then. 

However, same result, as before. Thanks for pointing this out anyways, Melody. 

What would be the height of the tank if it is 50cm wide and 60cm long and it can hold up to 126 liters of water but they recommended filling it up to 2/3 of water?

This is a tricky question; here's how I undrestand it:

1liter = 1dm³ = 1000cm³

V = a * b * h

h = V / a * b

h = 126000cm³ /3000cm²

h = 42cm

The height of the tank is 42cm!                                                                                                                                                                                                                                                                                                                                           (The height of the recommended water level is 2/3 of 42cm, which is 28cm.)