In an active sentence we need to include the agent as subject; using a passive allows us to omit the agent by leaving out the prepositional phrase with by.
- Active: Jackson throws me into the dungeon.
- Passive: I was thrown into the dungeon by Jackson.
- Agentless passive: I was thrown into the dungeon.
The “prepositional phrase with by” is the phrase starting by which identifies the agent. In converting an active sentence to a passive, the agent is available and can be included as in the second example here.
The agent can be omitted if we leave out the phrase starting by (see the third example).
The textbook is not talking about the “into the dungeon” prepositional phrase, because that is not “the prepositional phrase with by”. It can be simplified using Edwin Ashworth's examples:
- Active: Marshall bowled Boycott.
- Passive: Boycott was bowled by Marshall.
- Agentless passive: Boycott was bowled.