Problem that I have forgotten the origin of :( ... found it:)

 Scrolling on UTube I found this problem, now I haven't watched this, the challenge is to solve it without being shown a solution.

This problem appears to have insufficient information to be able to solve. Which if it has a unique solution means it is constant for what ever  value/s we assume for the missing data.

If this is so a common approach is to use an edge case where the solution is easiest. Here the obvious edge cases are when the distance between the walls is zero or infinite. Examination of these edge cases seems to get us nowhere, so we could just assume some value for the separation of the walls and work with that. However I think we should deal with this in a more general way. So we produce a labelled diagram:

Now we see that $\triangle$AEF is similar to $\triangle$ACB, or $x/u=6/d$, and similarly $\triangle$BDEis similar to $\triangle$BEF, or $4/d=x/(d-u)$. 

This gives us $x=\frac{6u}{d}$ and $x=\frac{4(d-u)}{d}$ equating these and simplifying gives: $u=\frac{4}{10}d$. Substituting this back into the first of the equations for $x$ and simplifying gives the answere $x=\frac{24}{10}=2.4$

As a final check lets draw a scale diagram and measure $x$ (for some value of $d$) accepting there will always be some error in the diagram and hence in the measurement: