How long will it take garamycin (gentamicin) ophtmalic drops for an eye infection?

Depends. If your eye is infected with a susceptible bacterium, then the response will be rapid and you should notice improvent in 2-4 days. If you have the far more common viral infection, then the garamycin (gentamicin) will be irrelevant and the virus will run its usual course of 3-10 days.