Puzzle 24: Keep It Even

Take 16 objects (coins, checkers, etc) and put them in four rows of four each. Remove 6, leaving an even number of objects in each row and each column (ie. 2 or 4 objects in each row and column). There are many solutions.
Extension: Find all possible solution. Can you prove those are all of them?
Extension: Find all possible solution. Can you prove those are all of them?