These can be harder to spot than naked pairs or triples but the principle is essentially the same. Again it applies to rows, columns and subgrids but we will only consider one of those at a time.
You're looking for a quadruple of candidate numbers used in four different cells within the same column. As this quadruple of cells must contain all occurences of the four digits (but we don't know which order just yet), we can eliminate any other uses of the digits in the column.
This technique is also known as locked candidates and is essentially a variation of the pointing and claiming techniques, but with four digits at once.
N.B. You should only use this strategy once all cells in the column (or row or subgrid) have been filled with candidates.
In the example, the numbers 1, 3, 8 and 9 comprise a quad. The center cell only shows candidates 1 and 8 but we can still use it in the quadruple by imagining that 3 and 9 are also candidates and because there are no other possible numbers for the cell.
We can now eliminate any other uses of the digits 1, 3, 8 or 9 elsewhere in the column: