For the function x^2 + 2x - 4 ,

find lim f(h+4) - f(4) / h
h-->0

you should have

f(x) = lim ( f(h+4) - f(4) ) / h

= lim ((h+4)^ + 2(h+4) - 4 - (16 + 8 - 4))/h , as h --> 0
= lim( h^2 + 8h + 16 + 2h + 8 - 4 - 20 )/h
= lim h(h+10)/h as h ---> 0
= lim h+10
= 10