I have a spreadsheet with American date format. If I try to change the Date to European format it shows 10/4/2016 (american format) as 10th April instead of 4th October.
How do I convert the dates?
Quoting @bikermanirl: “If I try to change the Date to European format…”
How did you try?
Did you assume the date found to be a number? … to be text?
Did you decide this in any way? How?
What UI-language set for your install of LibO?
What locale chosen under ‘Tools’ > ‘Options’ ‘Language Settings’ > ‘Languages’ ?
Try this: in the cell format dialog, change the language on the Numbers tab to a European language, except for English(UK).
+1, but why except for English (UK) ?
Try it and see 
Changing the language changes only the presentation, so, you won’t loose anything.