(-28x³y³z + 34x³y³ - 4z) - (52x³y³z + 22x³y³ - 41z)

Remove the parentheses.  The first parentheses is understood to be 
preceded by a + sign so we leave all the signs inside just as they 
are when we remove the parentheses.

But the second parentheses is preceded by a - sign so we change all 
the signs inside when we remove the parentheses.  So we have this:

-28x³y³z + 34x³y³ - 4z - 52x³y³z - 22x³y³ + 41z

Now we rearrange the terms so that like terms are together

-28x³y³z - 52x³y³z + 34x³y³ - 22x³y³ - 4z + 41z

Combine the coefficients of x³y³z:  -28-52 = -80

Combine the coefficients of x³y³:  +34-22 = 12

Combine the coefficients of z:  -4+41 = 37

-80x³y³z + 12x³y³ + 37z

Edwin