Simple:
* I encountered a friendly dog on my walk.
* She encountered a problem with her computer.
More Complex:
* During our travels, we encountered breathtaking scenery and diverse cultures.
* The team encountered unexpected challenges during their research project.
* The journalist encountered resistance from the authorities when trying to report on the story.
Figurative:
* She encountered a wave of sadness after receiving the news.
* He encountered a moment of clarity during his meditation.
The specific sentence you need depends on the context you're writing in.