Expanding each set of parentheses using the distributive property:

(6y - 1)(2y - 8) = 12y^2 - 48y - 2y + 8 = 12y^2 - 50y + 8

(3y - 4)(4y - 2) = 12y^2 - 6y - 16y + 8 = 12y^2 - 22y + 8

Now we can subtract the second expression from the first:

(12y^2 - 50y + 8) - (12y^2 - 22y + 8) =

12y^2 - 50y + 8 - 12y^2 + 22y - 8 =

-50y + 22y =

-28y

So, the simplified expression is -28y.