As far as I understand what I read, Libya has its own calendar which starts from the year the prophet died (632 A.D) and which uses the Gregorian year and months (only having different names for the months).
So the 4/10, and then you need to add 632 to your year 1378, that's our current year 2010.

Please see reference below. To complicate matters, apparently Libya also has a Miladi calendar, which uses the same method but starts from the prophet's birth year.

To convert a Libyan year to a Gregorian date add 632 (the first year of the Libyan calendar is counted from the year Prophet Muhammad died):
24 Nasir 1369 (add 632) = 24 July 2001

To convert a Libyan miladi year to a Gregorian date add 570 (the year Prophet Muhammad was born):
24 Nasir 1430 M (add 570) = 24 July 2000

http://library.princeton.edu/departments/tsd/acm/appendix/mo...

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Note added at 18 mins (2010-12-16 11:56:49 GMT)
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Sorry, there was an incomplete sentence up there: "So the 4/10" --> So the day and month, 4/10, remain as they are..."