Just by looking at this over breakfast, no calculator to hand so I can't check the sums but IMHO I reckon C is most probably correct. Your 600 n.m. of eastbound flight at 6 degrees south covers more degrees of longitude than the opposite direction 600 n.m westbound at 4 north ( because the earth is "thinner" at 6 south than at 4 north
, i.e; the lines of longitude are closer together ) , therefore having flown your 600 n.m box you must end up east of where you started....
Edited to add:
After after closer inspection and another coffee I think it might be worth
taking a look at your leg two calculation:
I agree the leg starts at 0600S 17000
W, - the question states you fly
east for 600 nm.
You've written:
Flying 600nm East (600/cos6 = 10.055 deg. 170+10.055 = 180.055. 360-180.05= 179.9449) the position becomes 0600S 179.9449 E
I've emphasised a few points ....
, this might be a classic case of a quick picture or rough diagram being worth a thousand calculations.