Show that if K and N are normal subgroups of G, then K intersect N is normal to G.

We have gkg^-1 is in K and gng^-1 is in N.

I think I know the basic idea:

Take a h in the intersection and take an arbitrary g.

I need to show g^-1hg is in the intersection

I guess I'm stuck in showing that. I guess maybe I don't understand what taking that h means.