Domino

The excluded domino is number 2 and 2

By systematically checking all 28 possible dominoes in a standard double-six set (0-0 through 6-6, including all unique pairs), the domino [0,1] is the only one missing from the 27 dominoes shown in the image. All other combinations from the complete set are present.

After counting and verifying every tile in the image, the domino [6, 0] is the only one from the standard 28-tile double-six set that is missing.

Counting the pips on each half in the image shows the 3s and 4s each occur one fewer time than expected for a complete double-six set, so the missing domino is [3,4].

By analyzing all 27 dominoes in the image and comparing against the complete set of 28 double-six dominoes, I identified all dominoes containing 0 except [0,6]. The dominoes present include [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5]. The missing domino is [0,6] (blank paired with six dots). I can identify [0,5] in the fifth row, and all other 0-pip dominoes are accounted for in the visible set, leaving only [0,6] absent.