Make: Electronics (Experiment 11) LED blinks only once
You are correct in saying that the anode voltage is Vcd (Anode pin with reference to ground) and Vgh is the gate voltage (Gate pin to ground). That is the simple part.

Now, I cannot say immediately what is wrong. But a few things strike me as odd, so maybe we can work this through together.

If Vab is zero, Vcd must be roughly 12V, this stands true. But, Vef is 5V and Vgh is roughly 9V while there is no current through the LED (I am assuming it was off when you took these measurements). If no current is flowing through the LED, I would think that Vef+Vgh would also amount to 12V. 

Now, since Vcd is 12V, this means that the capacitor is fully charged. Which makes sense. Now, we would like this to discharge, but it's not. So I would expect that there is no path to ground in order to discharge. The original schematic doesn't say where the gate or anode should go. Maybe the 2N6027 isn't properly setup? 

I would recommend going over the data sheet for the 2N6027 if you haven't already. Looks like it should behaving something like a switch, i.e. Once Vcd reaches a certain value "turn on" and allow discharge, which would illuminate the LED.

Hope this helps. Let me know if you have more questions, I will do my best in being prompt with helping in any way.

Good luck! 
- Josh