The solution set of $6≤ -3(2x-4) < 12, x∈R$ is:

(0, 1]

The correct answer is Option (1) → (0, 1]

Given inequality: $6 \le -3(2x - 4) < 12$

Divide all parts by -3 (reverse inequalities):

$\frac{6}{-3} \ge 2x - 4 > \frac{12}{-3} \Rightarrow -2 \ge 2x - 4 > -4$

Add 4 to all parts:

$-2 + 4 \ge 2x > -4 + 4 \Rightarrow 2 \ge 2x > 0$

Divide by 2:

$1 \ge x > 0 \Rightarrow x \in (0, 1]$