How to find the total resistance of this circuit
First, identify the nodes that are have the same voltage on one side and the same drop voltage on the other end. Take the parallel of the resistors and substitute that value for the R-equivalent.

If you redraw the circuit, you will see that voltage drop is the same for 


R6 and R1 path
R5 and R1 path
R4 and R2 path


Let's call the low side node, attached to the voltage source, X; and,
the upper side, where R5, R6 and R4 are connected, Y. The voltage drop across the aforementioned resistors are Vy-Vx, corresponding to the nodes at location high side Y and low side X.

Focus on this portion of the circuit and simplify:
Here we see R5 and R6 share the same node with R1. Call this node Z. These two are in Parallel, because R5 and R6 have the same voltage = Vy-Vz. Simplify these two resistors, and this becomes R56 equivalent. 

Now R56 is in series with R1; Simplify and substitute this with R561 and attach it between node Y and node X. 

R561 is parallel with R4 (and R2 along that path), b/c it is between nodes X and Y. Simplify this one and make the substitution.

The process is identifying the parallel combination of resistors and then resolving any series resistors attached. Make sure that when two or more resistors are in parallel, we can identify the total voltage across to be the same. In your example, it is easy to identify R5 and R6 in parallel, but to identify (R5||R6 + R1) || (R4+R2) is not so easily seen.

Redraw the circuit each time you simplify with an equivalent resistor. 

The rest is left as an exercise. :)