Explaining a gap after caregiving or layoff (Louisville)

I have been out of work for 4 months and worry about the gap. I would rather hear the honest version than the polite one. I am not sure how much to explain. What do you say in interviews?

Thanks for writing this out. I went through something close to it 4 months ago, and it got easier once I kept a simple log of every call and form.

I was hired after a 4-month gap. The manager said the skills test mattered more than the dates.