Ah okay, I think I get what you mean now.
Well, you have 3 gates ... not just 1. All with a different propagation delay, so you have to work out all the changes in sequence.
Any change on the A and B port will take 20 ns before the change arrives at "e". And after the change arrives at point "e" it will take an ADDITIONAL 20 ns before it will arrive at point. So suppose you make only a change at port A, then it will take a total of 50 ns before the effect of this input reaches the "x" output.
And to make things a little more difficult, you have 3 changes all at once. Now since AB goes from 00 to 11 through an AND gate that makes it a bit easier.
At t=0 changes from AB=00 to AB=11, so at t=30 this reaches the output of the AND gate (point "e").
Similar story for C ...
At t=0 C changes from C=0 to C=1, so at t=10 this reaches the output of the NOT gate (point "y").
You just work out the e, x, y results for every 10 ns step and you'll see what is happening.
Hope that helps.