Paper-folding questions usually ask how a mark or hole appears when a folded sheet is opened. A dependable method is to undo the folds in reverse order, reflecting the existing marks across the fold line each time.
Work through a two-fold example
Take a square sheet represented by coordinates from 0 to 4 on both axes. Fold the left half onto the right along x = 2. Then fold the bottom half onto the top along y = 2.
The folded sheet occupies the top-right quarter. Punch a hole at (3, 3), away from either fold line.
Undo the last fold first
Opening the horizontal fold creates its mirror at (3, 1), alongside the existing hole at (3, 3). Now open the vertical fold. Those two points reflect to (1, 3) and (1, 1).
The unfolded sheet has four holes: (3, 3), (3, 1), (1, 3) and (1, 1). They are symmetric about both fold lines.
Why simply doubling can fail
A punch directly on a fold line can coincide with its reflected position. Boundary cases may therefore produce fewer distinct locations than blindly multiplying by two at each stage.
Track positions, not only counts. A choice with the right number of holes can still put them in the wrong places.
Keep the fold direction and line separate
The fold line determines the reflection. The folded region tells you which layers are present at the punch. Read the diagram's arrows carefully before beginning the reverse process.
A final symmetry check
For the example above, every hole should have a partner reflected across each fold line. If one corner has no matching partner, revisit the unfolding step.
During practice, sketch intermediate stages rather than jumping directly from the folded picture to the final answer. The intermediate representation makes it easier to see which reflection created each mark and where a mistaken location entered the solution.