Domino

The excluded domino is number 2 and 1

After listing and counting all 27 dominoes present in the image against the full double-six set, the [6, 4] (or [4, 6]) domino is the only one missing.

After systematically identifying all 27 dominoes present in the image, I verified against the complete standard set of 28 dominoes. The domino [4, 4] (double four) is the only tile missing from the set. All other combinations of numbers from 0-6 are represented.

I systematically catalogued all 28 dominoes in a standard double-six set and compared them to the 27 dominoes shown in the image. After identifying each domino tile visible in the image, the tile [0,5] (blank-five) was not present among the 27 shown dominoes.

I examined the 27 tiles and could not find the double-five tile (5-5); all other combinations from 0 to 6 appear to be present.

By counting the occurrences of each number across all halves in the image, numbers 0-3 and 6 appear 8 times each, while 4 and 5 appear 7 times each, indicating the missing domino is [4|5].

By systematically identifying all visible dominoes, I can see all combinations of 0 with numbers 0-5 present: [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5] are all visible in the image. The domino [0,6] would have one blank half and one half with six dots. Scanning through all 27 dominoes, none contain a 6-dot half (which has a distinctive pattern of two vertical columns of three dots). Since all other 0-series dominoes are present and accounted for, the missing domino must be [0,6].