When is it found difficult to evaluate the exact cost of risk which of the following is the best method to evaluate on?

If you cannot evaluate the exact cost of risk, chances are that you are not seeking quantitative method. Numerical and qualitative basis are effective based on input from Subject Matter Experts. However, Avoidance basis can be biased, in my opinion. I would rather look at a risk on qualitative basis (assuming quantitative data is insufficient) and determine the consequences of each individual risk factor, than to term risks based on avoidance basis. However, if the project is small and familiar, avoidance basis could be used.  

Surely all risk assessments and analysis are based on avoidance / prevention first and then damage control 

of other factors such as financial, numerical, qualitative after?

Appreciating Fatema Tuz Zohra's answer, I would say C - Qualitative basis is the correct answer. 

Thank you for the invitation

Thank you for your question

An answer was agreed Option C

With greetings and appreciation

Avoidance comes first to evaluate any risk. All the remaining methods are run only after the failure of aviodance of risk

Qualitative is the best when the assessment of exact cost is difficult

Cost is a nemeric factor derives from various means. But when we dont know the outcome of an event ( say Legal litigation/event which entity has never experienced earlier), it increases the difficulty level to predict the cost. However, the easiest way to predict cost is "use deterministic method" ( Regression or Linear programming). Number derives from probabilistic way always put risk management team in dilemma to provide reasonableness of the probability.