To calculate the value of the expression:

4 cos(-8π/3) ctg(-3π/4) sin(3π/2)

First, we calculate the value of each trigonometric function:

cos(-8π/3) = cos(2π - 8π/3) = cos(2/3π) = cos(π/3) = 1/2 (since the cosine function has period 2π)

ctg(-3π/4) = ctg(-3π/4 + π) = ctg(π/4) = 1 (cotangent function is equal to 1 at π/4)

sin(3π/2) = sin(π/2) = 1 (the sine function is equal to 1 at π/2)

Now, we substitute these values back into the expression:

4 (1/2) 1 * 1 = 2

Therefore, the value of the expression is 2.