The Quadro constraint is global. In the entire grid, every 2x2 set of cells contains at least one odd digit and at least one even digit.
Another way to say this is that no 2x2 set of cells contains only even digits or only odd digits.
It might be tempting to try to solve this using only the green lines, with the pair of odd and pair of even cells to close the deal. But let the odd and even cells remind you: this is a quadro puzzle. The 2x2 rule will help!
Three of these things belong together / three of these things are kind of the same // Can you guess which one of these doesn’t belong here? / Now it’s time to play our game // It’s time to play our game
It’s less common in the world of Sudoku, but many pencil puzzles have a “2x2” rule, although most of those involve “shaded” and “unshaded” cells. We don’t do shading in Sudoku-land, so it’s Odds and Evens instead. You can shade or color it if you like, so long as you break up every 2x2 set of cells.