g(-5) is like g(x) but 5 is instead of x. So to figure it out, just put 5 instead of x in the g(x) function. Since the g(x) function is x^2-8x+21, when you substitute 5 into the function you get
5^2 - (8*5) + 21.
When you simplify that, you get
25 - 40 + 21 = -15 + 21 = 6
g(x+4) is the same thing. Just put (x+4) instead of x in g(x) function to get
(x+4)^2 - (8*(x+4)) + 21.
When you simplify that by multiplying, distributing, and combining like terms, you get
(x^2+8x+16) - (8x+4) + 21 = x^2+8x+16 -8x-4 +21 = x^2 + (8x-8x) + (16-4+21) = x^2+33
Hope this helps.