Any number with a つ attached to it means you are counting that number of things. In this case, it's six things.
Since this word consists of a kanji with hiragana attached, you can guess that it uses the kun'yomi reading. Here's a mnemonic to help you do that:
What are the six things that you need to count? This time you are counting six cows. The reason it's six is because you wanted exactly six moos (むっ). No more, no less. You're very particular about your moos.
There are six spoons.
The meeting room has one table and six office chairs.
I ordered six wine glasses.