Topic: Group verb,

Best Answer Explained in Below-:

The phrase "The waiter took the plates --- after we had finished eating" requires a preposition that conveys the action of removing the plates from the dining area. Among the options given—off, up, away, and out—only "away" accurately reflects this context.

1. **Off**: This term typically suggests detaching something from a surface, but it does not inherently imply removal from a space. For instance, "take the plates off the table" could work in a slightly different context but doesn’t fit well here after a meal.

2. **Up**: This word often indicates lifting or raising something but does not suggest an overall removal from a setting or location. You wouldn’t say "take the plates up" in this context.

3. **Away**: This option signifies taking something from one place to another, effectively communicating the idea of clearing the table post-meal. It indicates that the plates are being removed from the patrons’ immediate vicinity, aligning perfectly with the action of a waiter clearing dishes.

4. **Out**: While this can suggest removal, it implies going outside or perhaps removing items from a particular space, which doesn’t fit here as well as "away."

Thus, "away" is the most suitable choice, as it clearly denotes the action of the waiter clearing away plates following the meal.