You know that to get from A to E you start from A, and travel [15,-20,0] to get to E.
As AE is a line, you can add in a variable lambda to the equation to get any point along that line or, if you change the start point (from A to B) to get any point on any parallel line (such as D)
The actual equation for A to E specifically is [0,0,6]+[15,-20,0]. You can take out a multiple of 5 to make it [0,0,6]+5[3,-4,0].
The [3,-4,0] is the direction vector. 5 multiples of it will allow you to travel the 25 metres from A to E. By this logic, you need 3 multiples of it (lambda=3) to travel 15 metres; the distance BD.
Simply combine this knowledge of BD=3[3,-4,0] with your start-point (B) and you'll arrive at D.
Edit: It wasn't a stupid question; vectors are hard concepts to get. I take further maths aswell, and one of our modules is entirely upon vectors, but I still struggle with the C4 stuff. Some people find it easy to visualise, others prefer other kinds of math, such as mechanics or statistics.