let the equation be f(x)= ax3+bx2+cx+d..
Give f(-1)=10=> -a+b-c+d=10
f(1)=-6=>a+b+c+d=-6 =>b+d=2
a+c=-8
also maxima of f(x) at x=-1
=>f'(-1)=0( f('x)=3ax2+2bx+c) or 3a-2b+c=0
and minima of f'(x) at x=1
=>f"(1)=0(f"(x)=6ax+2b) or 6a+2b=0 or b=-3a =>a=1,b=-3,c=-9 and d=5
hence substitute and find
if you want i can work that too:)