Let:
\(R1 = 18\Omega\\R_2 = 12\Omega\\R_3 = 9 \Omega\\R_4 = 6\Omega\\\)

If I assume \(R_1 & R_2\) are in series and \(R_{12}\) in parallel with \(R_{34}\) the equivalent resistance is correct but I have no solid reasoning behind this conclusion. As I see it the current in the top node connecting \(R_1 & R_2\) has two paths to choose from?

 

Perhaps it will be more clear if you redraw the circuit like this:

 

Perhaps it will be more clear if you redraw the circuit like this:

Thank you, probably need to get more exercise reducing those slightly more complicated resistance problems but that made it completely clear.

 

Never be afraid to resketch a circuit in a configuration that makes more sense to you. The human brain is very good at pattern recognition, but that works against us when we see a new pattern that is really just a redrawing of a different pattern -- our brain insists that it is a new pattern with no relationship to previous patterns and we tend to accept it. But as we redraw a circuit, that same tendency biases us toward using patterns with which we are already familiar, enabling us to see them.