You wrote that you drew a line parallel to the left side from the top-right corner down to the base. That line will also be split into lengths of exactly $3$ and $2$, just like the left side. This is because you have parallelograms on the left. This mean that the ratios on the triangles on the right is $3:(2+3)$, and this gives you that the right hand side of the trapezoid is $4*5/3=20/3$, making $f=20/3 - 4 = 8/3$.
To find $e$ you will have to make some assumption. From the right hand end of the horizontal line of length $6$, you can draw a line down to the base, parallel to the left side of the trapezoid. To the left of that line you have a parallelogram, so that line is of length $2$, and the part of the base to the left of it is of length $6$. So to find $e$, you need the part of the base to the right of it. That unknown part is the base of a triangle with sides $2$ and $f=8/3$. Unfortunately, it is impossible to find that third length unless we know one of the angles of that triangle.
To illustrate this, I have drawn the diagram in two ways:
You can clearly see the length of the base $e$ differs, even though the given lengths and the length of $f$ all remain unchanged.
Presumably the left side is supposed to be perpendicular to the base. In that case you can use Pythagoras to find out the exact length.