Domino

After cataloging all 27 visible dominoes from the double-six set, which consists of 28 tiles, the double-six [6,6] is the only tile not present in the image.

The excluded domino is number 2 and 2

By systematically examining all 27 dominoes visible in the image and comparing against the 28 tiles that should exist in a standard double-six set (all combinations of numbers 0-6), the domino [4, 4] is not present. All other dominoes including [0, 0], [1, 1], [2, 2], [3, 3], [5, 5], [6, 6] and all mixed combinations are accounted for in the image.

Counting the pips on each half in the image shows the number 6 appears only six times while every other number from 0–5 appears seven times, so the missing tile must be the double six [6,6].

By systematically accounting for all 28 dominoes in a standard double-six set and identifying the 27 dominoes visible in the image, the missing domino is [0,6]. This can be verified by checking that all other dominoes involving 6 are present: [1,6] (row 6, position 2), [2,6] (row 5, position 5), [3,6] (row 3, position 5), [4,6] (row 4, position 1), [5,6] (row 5, position 1), and [6,6] (row 5, position 1 or row 4, position 1 depending on orientation), while [0,6] with a blank half and a 6-dot half is absent from the grid.