Simplify RCL Circuit
Note: Russell has a nice solution, which is simpler than mine, but only works if the problem is made for it (i.e. a trick question), while my solution is more generally applicable. I guess it depends on how far you got in your circuit analysis class. If you have the feeling this kind of circuit is over your head the professor probably made it a trick question with a simple solution.  

Starting from the left you have a triangle L-2L-C. You can transform this using a delta-star transformation. Write down the transformation formulas from delta to star and vice versa in big letters, you're going to need them. Applying those you get an impedance in series with the 2C on the left, and the other legs of the star will be in series with the 3R+3R and 2R+R, resp. If you redraw your schematic at this stage you'll see a new triangle or delta, this time with the 2C in the center of your schematic as one of the sides. Again apply the delta-star transformation. A few more steps and some parallel impedances and everything is just one long chain.