the "mode" is the value that occurs most often

the mean is 4 thus 2 out of 3 numbers are equal to 4

now we know that the 3 numbers are: 4, 4 and x, we need to find x

the "mean" ("average") is the sum of a set of data divided by the number of data

the mean is 6 thus

(4 + 4 + x)/3 = 6

by solving the equation we find

x = 10

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the three numbers are 4, 4 and 10.