Answer
The battery can deliver energy at the rate of $100~W$ for $~~14.4~hours$
Work Step by Step
We can find the total charge in coulombs:
$Q = (120~C/s\cdot h)(\frac{3600~s}{1~h}) = 432,000~C$
We can find the initial energy stored in the battery:
$E = \Delta V~Q = (12.0~V)(432,000~C) = 5,184,000~J$
We can find the time that the battery can deliver energy at the rate of $100~W$:
$t = \frac{Energy}{Power} = \frac{5,184,000~J}{100~W} = 51,840~s$
We can express this period of time in units of hours:
$t= (51,840~s)\times (\frac{1~h}{3600~s}) = 14.4~h$
The battery can deliver energy at the rate of $100~W$ for $~~14.4~hours$.
