Hannah can paint a room in 15 hours thus in 1 hour she can paint 1/15 of a room

Destiny can paint the same room in 12 hours thus in 1 hour she can paint 1/12 of a room

let 'x' represent the number of hours both Hannah and Destiny need to paint the room together

Hannah and Destiny together in 1 hour will pain 1/x of a room

This means that:

1/15 + 1/12 = 1/x

by solving we find:

x = 20/3 hr

x = 6 hr (2/3)*60 min

x = 6 hr 40 min

Hannah and Destiny need 6 hours and 40 minutes to paint the room together.