I need assistance identifying the farthest observations from the mean in the attached histogram image?

Hello!
Although the range is from 1 to 6, the mean and the distances from the mean are computed using the vertical values (those below 0.2). They are relative frequencies (probabilities) of the corresponding outcomes. Note that the horizontal values could be even non-numeric (for example, if the die would be marked with letters, not digits).
The mean is the arithmetic mean of the values. We cannot compute it because there are no enough marks on the vertical axis. But we can determine what observations (outcomes) are the farthest from the mean: they are the observations with the maximum frequency and with the minimum frequency.
At the given graph, they are 5 (the outcome with the highest bar) and 6 (the outcome with the lowest bar). The relative frequencies of other outcomes are closer to the mean.
The answer: 5 and 6.
 
https://www.mathsisfun.com/data/relative-frequency.html