Why the tray only holds six
The puzzle is not the match. It is which free tile you spend a slot on.
A Tile Tree board is built in triples: every picture on the level appears three times, or a multiple of three, so a careful sequence can clear it. The pressure comes from the tray.
Six slots sounds roomy until two pairs are waiting and the third copy of each is still buried. Take the wrong free tile and those pairs become a crowd. Fill all six without a match and the level stops.
That is why Hint, Undo, and Hammer exist. Hint glows a free tile and prefers one that already has a partner in the tray. Undo puts the last pick back on the board. Hammer removes one free tile without spending a slot. Shuffle is the odd one out: it keeps every tile in place and swaps the pictures among the tiles still on the board, which can uncover a match you did not have a moment ago.
The lose screen is not a hard stop. Retry starts the board again. An optional rewarded ad can continue by returning the last tray tile when that pick is still recorded. If it is not, the continue removes one tile from the tray instead.
None of this asks you to swap neighbours the way a classic grid match-3 does. You are peeling a stack, and the tray is the only score that matters until the board is gone.