As the others say, 'didn't' is the correct answer. Let's look a little more closely at the grammar. Often in English we use the auxilary verb to stand in for the complete phrase. Think of some basic examples that you learnt when you began to study English. For example: "Do you like oranges?" "No, I don't." In this example you understand automatically that 'I don't' is a shortened version of 'I don't like oranges'. Because we have the context, we don't have to repeat the full verb phrase. The example you have given is exactly the same, just at a higher level. Grammatically, it would be completely correct to say 'Jack was supposed to call me last night. I wonder why he didn't call me.' However, this is an unnecessarily long way to express it, and so we drop off the final verb phrase and only keep the auxilary verb, 'didn't'.

The first sentence is correct. "Jack was supposed to call me last night. I wonder why he didn't". "didn't" is required because you need a verb that means 'perform an action' which in this example is "to call me last night". 'do' means to perform an action, so the past tense 'did' works here) "Jack was supposed to call me last night. I wonder why he didn't call me"

"Didn't" is correct. You're saying that Jack "didn't" call you, and you wonder why. You're not saying that he "wasn't" supposed to call you. He was supposed to call you, but he did not call you. So you wonder why he "didn't" call.

A correct example of wasn’t: Jack was supposed to be at the game last night. I wonder why he wasn’t (“at the game last night” is implied).