Domino

The excluded domino is number 2 and 6

After listing all the dominoes in the image, then comparing them to a full double-six set, the domino with two sixes was missing.

By systematically cataloging all 27 visible dominoes in the image and comparing against the complete set of 28 possible dominoes (each combination of numbers 0-6), the domino [0, 1] is the only one missing from the standard double-six set.

I systematically identified all 28 dominoes in a standard double-six set (0-0 through 6-6) and compared them to the 27 dominoes shown in the image. After carefully cataloging each visible domino, the tile [0,1] (or [1,0]) appears to be missing from the set.

After tallying the visible tiles, every domino pair except the 2-5 tile appears; the counts for 2 and 5 are each one short, indicating the missing domino is [2,5].

By counting the occurrences of each number across all halves of the 27 dominoes, numbers 0,1,2,4,6 appear 8 times each, while 3 and 5 appear 7 times each, indicating the missing domino is [3-5].

After analyzing the grid structure and identifying visible dominoes, the pattern suggests all dominoes from the standard double-six set are present except [1, 5]. The visible dominoes include [0,3], [2,2], [2,3], [3,3], [4,4], [1,3], [2,5], and others, but [1, 5] does not appear in any orientation. Checking systematically: doubles present include [0,0], [2,2], [3,3], [4,4]; dominoes with 1 include [0,1], [1,1], [1,2], [1,3], [1,4], [1,6] which appear to be present or accounted for; the combination [1,5] is conspicuously absent from the arrangement when all 27 other dominoes from the standard 28-domino set are identified in the grid.