Learn Hardcore German: Was meinst du?

In Was meinst du?, was functions as the direct object of the transitive verb meinen, so it is in the accusative case. However, since was has the same form in both nominative and accusative, it remains was.

Why is the verb meinst in the second position, before the subject du?

German main clauses with a question word follow the V2 (verb-second) rule: the question word (was) is first, the conjugated verb (meinst) must come second, and the subject (du) follows.

What’s the difference between Was meinst du? and Was denkst du?

Both can be used to ask for someone's thoughts, but:

Was meinst du? focuses on opinion or meaning (“What do you think/opine?” or “What do you mean?”).
Was denkst du? emphasizes the thinking process or belief (“What do you think/consider?”).
Often they overlap, but if you want to stress “opinion” use meinen. You can also add dazu for “about it”: Was meinst du dazu? / Was denkst du dazu?.

How would I ask Was meinst du? in a formal or plural situation?