Notes:

The Himalayas are not that long and I don't think they did any mountaineering. That said, Biden's quote actually makes sense in context (that most people don't include for some reason):

And, folks -- (applause) -- let me close with what I’ve long said: America is a nation that can be defined in a single word. I was in the foothi- -- foot- -- excuse me, in the foothills of the Himalayas with Xi Jinping, traveling with him. (Inaudible) traveled 17,000 miles when I was Vice President at the time. I don’t know that for a fact.
And we were sitting alone. I had an interpreter and he had an interpreter. And he looked at me. In all seriousness, he said, “Can you define America for me?” And I said what many of you heard me say for a long time. I said, “Yes, I can, in one word: possibilities.” (Applause.) “Possibilities.” That, in America, everyone should be able to go as far as their hard work and God-given talent will take them. And possibilities. We’re the only ones. That’s why we’re viewed as the “ugly Americans”: We think anything is possible. (Laughter.)