My visual estimate is that if you "drop" the arrow head of w along a perpendicular to v, you hit v at about 4/10 the length of v. So k is about 0.4 and kv = 0.4 (6, 4, 2)T = (2.4, 1.6, 0.8)T
It turns out that I was grossly wrong. Hope you did better.
The visual approach to 3D problems is hard, unless you actually have a 3D image in front of you. The correct answer calls for some figuring:
What is u, where u + kv = w? (In the diagram u is the dotted black line).