{(x+2)(x-6)<(x+2)(x+1)+4 {2(6x-1)>7(2x-4)

Let's solve each inequality step by step.

Inequality 1: \((x+2)(x-6)<(x+2)(x+1)+4\)

1. Expand both sides:
   Left side: \((x+2)(x-6) = x^2 - 6x + 2x - 12 = x^2 - 4x - 12\)
   Right side: \((x+2)(x+1) + 4 = (x^2 + x + 2x + 2) + 4 = x^2 + 3x + 2 + 4 = x^2 + 3x + 6\)

   Now, the inequality becomes:
   \[ x^2 - 4x - 12 < x^2 + 3x + 6 \]

2. Subtract \(x^2\) from both sides:
   \[ -4x - 12 < 3x + 6 \]

3. Rearranging:
   \[ -4x - 3x < 6 + 12 \]
   \[ -7x < 18 \]

4. Dividing by -7 (which reverses the inequality):
   \[ x > -\frac{18}{7} \]

Inequality 2: \(2(6x-1)>7(2x-4)\)

1. Expand both sides:
   Left side: \(2(6x - 1) = 12x - 2\)
   Right side: \(7(2x - 4) = 14x - 28\)

   The inequality now becomes:
   \[ 12x - 2 > 14x - 28 \]

2. Rearranging:
   \[ 12x - 14x > -28 + 2 \]
   \[ -2x > -26 \]

3. Dividing by -2 (which reverses the inequality):
   \[ x < 13 \]

Conclusion

Combining the results from both inequalities:

1. From the first inequality: \(x > -\frac{18}{7}\)
2. From the second inequality: \(x < 13\)

Thus, the solution to the compound inequality is: \[ -\frac{18}{7} < x < 13 \]