Mode and Mean

I received a question that says

Find three numbers which have a mode of 4 and a mean of 6

Answer: Since the Mode is 4 then we have more than a 4. Either two 4s or three 4s but three 4s don't give a mean of 6 but a mean of 4.

So we have 4,4,x with a mean of 6

(4 + 4 + x)/3 = 6

8 + x = 18 x = 10

The three numbers are 4, 4, 10