I'm trying to solve the network below using a Delta-Y conversion of the upper 2k, 1k, 1k resistors. Note: I know that it could be solved using for example KCL.

I solved it as follows and got R_eq = 1.557... Kohms but their answer is 1.18Kohms, what am I doing wrong?

 

Doing a delta-wye conversion on the lower half would be much simpler since all three resistors would be 1 Ω. Doing that you can solve it without a calculator in just two or three lines and get an equivalent resistance of 13/11 kΩ (which matches their 1.18 kΩ).

You need to do sanity checks on your work.

If all three resistors in your delta were 1 kΩ, then all three resistors in the wye would be 1/3 kΩ. If all three resistors in your delta were 2 kΩ, then all three resistors in the wye would be 2/3 kΩ. That means that you would expect smaller values than you obtained. Note that a subtle point is that you don't necessarily expect all three values to be between 1/3 kΩ and 2/3 kΩ because of the nature of how increasing the resistance on one side of the delta drives down the resistance on the opposite leg of the wye.

Since you didn't show your work on how you obtained your equivalent wye resistances (which, considering that the whole point of your question was for us to tell you what you are doing wrong in your delta-wye conversion, seems a bit short-sighted, doesn't it) we can't tell you what you did wrong (without invoking our crystal balls).

Perhaps you might read up on delta-wye conversions:

http://www.allaboutcircuits.com/technical-articles/delta-wye-transforms-behind-the-scenes/