In Mahjong Solitaire, you remove tiles by matching pairs. Only "free" tiles can be played, and only identical tiles form a valid pair. This article explains how tile matching works and how it ties into strategy. For tile types, see Mahjong tiles guide; for terms, see Mahjong terminology.
Free Tiles: The Rule
A tile is free only if (1) no other tile lies on top of it, and (2) it has at least one long side (left or right) not blocked by the layout. Tiles under others cannot be played until the tiles on top are removed. Tiles with both sides blocked cannot be played until the layout changes. So matching always involves two free tiles. For the full rule set, see Mahjong Solitaire rules and Mahjong rules.
What Makes a Valid Pair
Two free tiles match if they are the same type: same suit and rank (e.g. two Character 4s), or same honor (two North Winds, two Green Dragons). Flowers usually match any flower; seasons match any season (implementation may vary). You click one free tile, then another; if they match, both disappear. For suit and honor details, see Mahjong tiles guide. For how to use this in play, see how to play and strategy tips.
Strategy and Blocking
Because only free tiles can be matched, the order in which you remove pairs matters. Removing a pair that uncovers new tiles gives you more options later. Removing a pair that blocks a unique tile can deadlock the game. So strategy is about which pair to take next. See winning strategies and mental focus for more. Tile matching is the core mechanic; the rest is planning.