The thing about an equation like 2x-3y+z-6=0 is that if you look carefully, there's a dot product hiding in plain sight. The equation can also be written
which means that if you take any point (x,y,z) in this plane, subtract the point (0,0,6), then the resulting vector is orthogonal to the vector〈2,-3,1〉. The vector 〈2,-3,1〉 called a normal of the plane. Conveniently, to find the minimum distance between a point and the plane, we need only subtract (0,0,6), dot with the plane normal, take the absolute value, and divide by the magnitude of the plane normal.
(-2,0,3) - (0,0,6) = 〈-2,0,-3〉
〈-2,0,-3〉 • 〈2,-3,1〉 = -7
||〈2,-3,1〉|| = ✓(14)
The distance is 7/✓(14) units.