The correct option is D drinking
Let’s examine the sentence: “I am not used to ______ strong coffee.” The sentence specifies habit of ‘drinking’ and not the action of ‘drinking,’ and so it requires a noun or a gerund in the blank. The gerund always has the same function as a noun (although it looks like a verb). The gerund ends in ‘ing.’ As Option B fulfils this requirement, so it is the correct answer. All the other options cannot be used as they would make the sentence meaningless.