In simple harmonic motion (SHM), the acceleration of a particle is directly proportional to its displacement but in the opposite direction. Looking at the options provided:

Option 1: ax = +3x

This equation does not follow the criteria of SHM because the acceleration and displacement are in the same direction.

Option 2: az = +3t^2

This equation is not related to displacement and does not follow the criteria of SHM.

Option 3: No equation provided.

This option does not provide any information to determine if the particle is executing SHM or not.

Option 4: ax = -x

This equation follows the criteria of SHM. The acceleration is directly proportional to the displacement, and they are in opposite directions. Therefore, option 4 is the correct answer.

Overall, option 4 is the only option that satisfies the requirements for executing simple harmonic motion.