Solve the compound inequality and give your answer in interval notation. \[ 4 x+4<3 x+10 \text { AND } 2(-6 x+2)+8 \leq-4 x+36 \]

Step 1 ：\(4x + 4 < 3x + 10\)

Step 2 ：\(x + 4 < 10\)

Step 3 ：\(x < 6\)

Step 4 ：\(2(-6x + 2) + 8 \leq -4x + 36\)

Step 5 ：\(-12x + 4 + 8 \leq -4x + 36\)

Step 6 ：\(-12x + 12 \leq -4x + 36\)

Step 7 ：\(12 \leq 8x + 36\)

Step 8 ：\(-24 \leq 8x\)

Step 9 ：\(-3 \leq x\)

Step 10 ：\(-3 \leq x < 6\)

Step 11 ：\(\boxed{-3, 6)}\)