Hello Paul,
Time zone difference calculations are not that difficult, but still in their more common forms contain a few potential stumbling blocks; once you throw the International Date Line (IDL) into the equation, those stumbling blocks tend to become more prominent. I had a go, though, and came up with the following:
When the plane takes off from American Samoa, just east of the IDL in GMT -11, at 23:30 on the Tuesday, it is already 22:30 on Wednesday in Fiji, which is west of the IDL in GMT +12. When it touches down in Fiji after the two hour flight, it would thus be in the wee hours of Thursday morning, at 00:30, there, while back in American Samoa it is then only 01:30 on Wednesday morning, i.e. 23 hours earlier.
I should in all honesty add that my geography is not that good that I knew off the top of my head that American Samoa sits where it does in relation to the IDL; however, I do know that the IDL runs a zig-zag course down the Pacific, so from the way the question was formulated I strongly suspected that such woukl be the case, and quickly verified my suspicions by looking up the IDL in a well-known Internet encyclopedia … 
The actual calculations are all my own, though …
/Mattias
Edited By Banjoman on 27/08/2015 09:12:18
Edited By Banjoman on 27/08/2015 09:12:32
Edited By Banjoman on 27/08/2015 09:12:51
Edited By Banjoman on 27/08/2015 09:13:34