Step by step:
Most importantly, you need to realize that this problem has nothing to do with springs (no K constant is given). This is a momentum problem. Same as if the one blocks "exploded" into two pieces. That kind of problem.

1. We know that p_y = mv and that p_y is preserved. At the highest point of trajectory, p_y = (8)(0). After the two blocks are untied, it becomes p_y = 4(v_1) + 4(v_2). Because we're finding the center of mass, no matter what which the spring was facing when it pushed the two blocks apart, the y velocity of the center of mass is 0.

Example 1: The blocks are pushed apart horizontally. Both of their y velocities are 0, meaning the center of mass velocity is also 0.
Example 2: The blocks are pushed apart vertically. One of their y velocities is 4, the other is -4. The center of mass velocity (4 + -4) / 2 is still 0.

2. Now that the explosion is done, we don't need to think about momentum anymore. We just know that the center of mass has a y velocity of 0, and essentially follows the same path as the object would've followed before springing apart. Therefore we find the velocity of the object after it's fallen for 2 seconds.
y_velocity = 0 + at
y_velocity = 0 + 9.8(2) = 20