The solution to the 4x4 Sudoku puzzle involves filling the empty squares so that each row, column, and 2x2 sub-grid contains the numbers 1 through 4 without repetition. The completed grid is as follows: Row 1 contains 3, 1, 4, 2. Row 2 contains 2, 4, 1, 3. Row 3 contains 1, 3, 2, 4. Row 4 contains 4, 2, 3, 1.