X-Wing (Size-2 Fish)

An X-Wing is a size-$2$ fish.

When a candidate digit $d$ in two rows or columns (the base set) falls only in two columns or rows (the cover set), then no matter how $d$ is placed, each of the two cover-set houses must contain exactly one digit $d$. Therefore, candidate digit $d$ can be eliminated from all other cells in the cover set.

For example, in the board below, take two rows as the base set. Look at candidate digit $2$ in row $4$ and row $7$: it appears only in column $2$ and column $5$. So regardless of how the two $2$s are arranged within row $4$ and row $7$, column $2$ and column $5$ must each contain one digit $2$. Therefore, in those two columns, candidate digit $2$ can be eliminated from every cell except the intersections of the base set and the cover set.

For another example, in the board below, take two columns as the base set. Look at candidate digit $6$ in column $2$ and column $5$: it appears only in row $5$ and row $7$. So regardless of how the two $6$s are arranged within column $2$ and column $5$, row $5$ and row $7$ must each contain one digit $6$. Therefore, in those two rows, candidate digit $6$ can be eliminated from every cell except the intersections of the base set and the cover set.