A cube.
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A square has 4 sides therefore 3 squares from 12 toothpicks will simply be three unconnected squares
Use squares and try it out for yourself. Get a number of squares and make a rectangle 3 squares long by 4 squares wide. Count the squares. You should have 12 squares (or 3*4). That's the best way I know to prove the formula.
Move 3 lines "from" - do you mean 'remove 3 lines from' - or - move 3 lines to other places? Anyway, this all depends on the layout of the five squares.