Final answer:
The correct term for the process of removing castings from their molds using vibrating equipment is called 'shakeout'. It is crucial for ensuring the integrity and proper shape of the final casting by removing sand or debris.
Step-by-step explanation:
The process of removing castings from their molds by using vibrating conveyors or tables is called b. Shakeout. During the shakeout process, the molds are vibrated to ensure that the castings are freed without causing damage or altering their shape. This is a critical step in the casting process as it ensures the final product meets the required specifications and is free of any sand or debris that could compromise its integrity.