One.
No, "does" cannot have two syllables. This is because your jaw only drops once when you say the word. The way I was taught however many times you say a word that is how many syllables there are in that word. Hopes this helps.
There are three Chinese syllables in the word "syllables."
The word 'answer' has 2 syllables. An-swer.
There are four syllables in the word "usually".
The word has three syllables.
The syllables in the word what is only 1 : "what".
The word apotex has three syllables. The syllables in the word are a-po-tex.
The word prophets has two syllables. The syllables of the word are pro-phets.
4 syllables are in the word di·ver·si·ty.
Their are two syllables in the word silly.
2 syllables are in the word nuisance. :)
2 syllables in the word weekend