U should use factor theorem
if x+3 is i factor of x^3+kx^2-8x+48 then on substituting x=-3 the value of polynomial will become equal to 0(u may ask why is that so in another thread or u may post it in the reply)
therfor (-3)^3+k(-3)^2-8(-3)+48=0 or -27+9k+24+48=0
or 9k=-45 therefor k=-5.