Distance between mode and mean = mode - mean

Distance between median and mean = median - mean

Given that,

(mode - mean) = k(median - mean)

⇒ mode - mean = k median - k mean

⇒ mode = k median - k mean + mean

⇒ mode = k median - (k-1) mean

Comparing it with empirical relation, i.e.

mode = 3 Median - 2 mode

We get,

k = 3