The first questions epistemology asks are: What can we know? and How can we know it? Those questions are, in my view, fundamental to any and every other philosophical argument. Knowing what is and is not available to knowledge, and being able to justify knowledge claims - is the essence of philosophy and the origin of wisdom.

I would object that epistemology itself is not a way of thinking that is either totally correct or incorrect, since there are many ways one can do epistemology. Epistemology refers to any number of ways in which one can think about knowledge.

Ask them to clarify the question. It's gibberish. Ask them to ask it again without using the words 'prove' and 'epistemology' and 'is the only correct way of thinking'.
Keep asking them this until something intelligible comes out of their face front.

Agreed. There is ambiguity in the question that could lead someone to misunderstand it.

Somebody asked me to "prove that epistemology is the only correct way of thinking".

What is my best way to respond to this? — Tommy Shiflett

“I wouldn’t know how.”

“Epistemology is a field of study not a way of thinking so wtf are you saying. And ways of thinking are not correct or incorrect, statements are correct or incorrect.”