Good for you helping your little brother!
This is just substitution of numbers into the variables.
I read the expression as 2x^2-2z^4+y^2-x^2+z^4, where ^ means “to the power of”.
Put x=-4 then x^2=(-4)*(-4)=+16; 2x^2=2*16=32; z^4=2*2*2*2=16; 2z^4=2*16=32; y^2=3*3=9.
Now put all these together: 32-32+9-16+16. 32 and 16 cancel out and we're left with 9. That's the answer: 9.