By definition;
m-n = -2.5 log (Fm/Fn)
Where,
m-n = 2.6 Mag
Fm/Fn = Flux ratio (to be calculated in this case).
Substituting all the values;
2.6 = -2.5 log (Fm/Fn)
2.6/-2.5 = log (Fm/Fn)
-1.04 = log (Fm/Fn)
Therefore;
Fm/Fn = Flux ratio = Antilog (-1.04) = 0.0912
Therefore the flux ratio of two stars, whose difference in magnitude is 2.6, is 0.0912