When to use cost of equity for discount factor and when to use WACC?

It depends on whether it is investment appraisal (and whether we want the APV as opposed to the NPV) or whether it is valuing a business. I do explain all the situations in my free lectures.

I cannot give you a rule because it depends on the type of question and what is specifically required. If you tell me a specific question that is giving you a problem then I will be better able to advise you :-)

The question asks you to calculate the adjusted present value, and for the APV we always discount at the cost of equity if all equity financed, and then adjust for the tax shield on debt.