vector question ??? please help?

A point on the line will be given by
x = 4s
y = 2s
z = s +1

Vector joining the above point and point A is (2-4s,4-2s,-6-s) (point of intersection)
Since this is perpendicular to line (reflection) (2-4s,4-2s,-6-s) dot (4,2,1) = 0 Find s.

Once you've s, you can find out the point of intersection. You can apply co-ordinate geometry here now since the point of intersection is bisection point of A and its reflection.