in hexagonl system face is (hkil) we know the formula h+k+i=0 by applying this we get -4= h,k=1,i=h which while Substituting -4+1+h=0. where h =3 is the answer
This Miller indices surely compatible with the hexagonal crystal system (as only this crystal system has four axes).
And as per properties of hexagonal crystal system, the sum of ...