The letter "X" shown to a hand's right indicates that the hand is an exposed hand, meaning you may call a tile and expose it to complete a pung, kong, quint, or sextet
If two identical tiles are discarded, one right after the other, and someone calls the tile for mah jongg, it is the 2nd discarded tile that can be claimed.
Several situations can make a hand invalid or no longer viable (i.e., dead), too many or too few tiles, picking from the wrong end of the wall, an invalid combination of exposures (including those from a concealed hand).