To solve this expression, we need to convert the trigonometric functions into their corresponding ratios.

ctg(43π/18) = 1/tan(43π/18)
tg(π/9) = tan(π/9)

Now, we can rewrite the expression as:

6(1/tan(43π/18)) - 4tan(π/9)

Next, we need to find the values of tan(43π/18) and tan(π/9) using the unit circle or a calculator.

tan(43π/18) ≈ -1.6
tan(π/9) ≈ 0.5774

Now, we substitute these values back into the expression:

6(-1.6) - 40.5774
= -9.6 - 2.3096
= -11.9096

Therefore, 6 ctg(43π/18) - 4 tg(π/9) is approximately equal to -11.9096.