What is the English translation of 'Cum dē hīs rēbus cognōvissēmus, statim castra mōvimus'?

The correct translation of 'Cum dē hīs rēbus cognōvissēmus, statim castra mōvimus' is "When we (had) learned about these things, we immediately moved (our) camp."

This sentence uses the subjunctive form 'cognōvissēmus,' which translates to "we had learned." The use of 'cum' along with the perfect subjunctive indicates a completed action that took place before another action — in this case, moving the camp. Therefore, the structure of the phrase supports the interpretation that the learning occurred prior to the moving of the camp, making "when we (had) learned" an appropriate choice. The subsequent clause "statim castra mōvimus" translates to "we immediately moved the camp," which effectively communicates the immediate action following the understanding of the events.

In contrast, other options either misplace the sequence of events or incorrectly interpret the grammatical structure employed in the original Latin.