Triangle xyz has vertices x(0,0), y(-4,0) and (0,6). find the coordinates of the orthocenter.

Orthocenter of a triangle is the point of intersection of all the altitudes of the triangle.
in this case, the altitude of XY is XZ, and the altitude of XZ is XY, and the two altitudes meet at the origin. 
so in this case, X(0,0) is the orthocenter