To understand sentence structure

Question

The quantifier we choose depends on whether it introduces a countable noun or an uncountable noun.

I don't understand this proportion "The quantifier we choose depends on....." because "choose" is a verb and "depends on" is a verb too.

Answer 1

• The quantifier we choose depends on whether it introduces a countable noun
  or an uncountable noun.

Sentences are not just words in a row. They are Constructions in a row. You use the term "proportion" as if it named the construction; it doesn't, so if you expected to apply whatever rules you may have learned about proportions, don't bother. You need to chop up the constituents of the sentence, which are mostly clausal and phrasal. Start with finding the [Subject] and the [Verb Phrase]:

• [The quantifier we choose] [depends on whether it introduces a countable noun or an uncountable noun.]

Both of these constituents are complex, and both have subordinate clauses attached, and both of them have had things done to them that's changed their syntax. The subject noun phrase the quantifier we choose contains a relative clause that we choose, with the that deleted, because it's not needed. I.e, it's really

• [[the quantifier][that we choose]]

Therefore choose is at the end of one clause, and that clause is the subject, and after the subject of the main clause comes the verb of the main clause, which is depends on, a verb with a transitivizing preposition on. So that's how come two verbs follow one another. One got stuck there at the end by the relative clause, and the other was coming up next.

There's lots more to comment on here in the Verb Phrase, but I'll quit with the question addressed.