To simplify the expression 4cos(4a) / ctg(2a) - tg(2a), we first need to rewrite the trigonometric functions in terms of sine and cosine:

ctg(2a) = 1 / tg(2a)
tg(2a) = sin(2a) / cos(2a)
cos(2a) = cos^2(a) - sin^2(a)
= 1 - 2sin^2(a)

Now we can substitute these expressions into the original expression:

4cos(4a) / (1 / (sin(2a) / cos(2a))) - (sin(2a) / cos(2a))
= 4cos(4a) sin(2a) / cos(2a) - sin(2a) / cos(2a)
= 4(2cos^2(2a) - 1) sin(2a) / cos(2a) - sin(2a) / cos(2a)
= 8 cos^2(2a)sin(2a) - 4sin(2a) - sin(2a)
= 4sin(2a)(2cos^2(2a) - 1) - sin(2a)
= 4sin(2a)(1 - 2sin^2(2a) - 1) - sin(2a)
= -8sin^3(2a) + 4sin(2a) - sin(2a)
= -8sin^3(2a) + 3sin(2a)

Therefore, the simplified expression is -8sin^3(2a) + 3sin(2a)