The simplest thing I can think of is using inclusion-exclusion.

Let A = event of rolling at least one 6, one 5, and one 4.

Let C = event that a 6 is not rolled.

Let D = event that a 5 is not rolled.

Let E = event that a 4 is not rolled.

Then by inclusion-exclusion,

Then you take

P(C) = P(D) = P(E) = ? (think about it)

P(C ∩ D) = P(C ∩ E) = P(D ∩ E) = ? (think about it)

P(C ∩ D ∩ E) = ?

See how far you can get.