I need help on this probability question. I would appreciate if someone could show me how to get the answer (with or without the answer I dont care)

This is a question about accepted idiomatic usage and level of formality rather than a question of grammar. These forms are not technically “grammatically incorrect,” but neither are accepted idiomatic usage. If you want to be fluent in your usage, and you are willing to come off as formal and a bit peremptory and demanding, you would say, “I would appreciate it if you …” But unless you want to convey impatient formality, you would probably want to say instead, “I would be grateful if you …”

You would probably never in any circumstance say "I will appreciate if you.." or "I would appreciate if you.."

Step-by-step explanation:

And you would also probably never even say "I will appreciate it if you.." This is just not the way English speakers speak. One reason you wouldn’t say “I will appreciate it” (besides the fact that it would sound impatient) is that you need to use the subjunctive “would” when you are using “if,” instead of the predictive “will.” You are only predicting that if a hypothetical event occurs, appreciation will occur. For instance: You impatiently say, “I would appreciate it if you would pay your rent.” You are predicting (or sarcastically claiming to predict) that if the rent is paid, you will be appreciative.