To determine the acceleration of the masses and the tension in the string, we can use Newton's second law of motion.

First, let's define the positive direction as the direction in which the 12 kg mass will move.

For the 8 kg mass:
The net force acting on the 8 kg mass is the tension in the string.
Using Newton's second law, we have:
Tension = mass x acceleration
Tension = 8 kg x acceleration (eq. 1)

For the 12 kg mass:
The net force acting on the 12 kg mass is the difference between the tension in the string and the weight of the mass. The weight of the mass is given by:
Weight = mass x acceleration due to gravity
Weight = 12 kg x 9.8 m/s^2

Using Newton's second law, we have:
Tension - Weight = mass x acceleration
Tension - 12 kg x 9.8 m/s^2 = 12 kg x acceleration (eq. 2)

Now, we can solve these two equations simultaneously to find the acceleration and tension.

From eq. 2, we can express the tension in terms of acceleration:
Tension = 12 kg x acceleration + 12 kg x 9.8 m/s^2

Substituting this into eq. 1, we get:
8 kg x acceleration = 12 kg x acceleration + 12 kg x 9.8 m/s^2

Rearranging the equation, we have:
-4 kg x acceleration = 12 kg x 9.8 m/s^2

Simplifying,
acceleration = (12 kg x 9.8 m/s^2) / (-4 kg)
acceleration = -29.4 m/s^2

The negative sign indicates that the 8 kg mass is moving in the opposite direction of the positive direction we defined earlier.

To find the tension in the string, we can substitute the acceleration value into eq. 2:
Tension - 12 kg x 9.8 m/s^2 = 12 kg x (-29.4 m/s^2)
Tension - 117.6 N = -352.8 N

Simplifying,
Tension = -352.8 N + 117.6 N
Tension = -235.2 N

The negative sign on the tension indicates that the tension is acting in the opposite direction of the positive direction we defined earlier.

Therefore, the acceleration of the masses is -29.4 m/s^2 and the tension in the string is -235.2 N.

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