Answer
$1677.72$ seconds
Work Step by Step
The graph with 12 nodes and each node having four choices will have $4^{12} = 16777216$ number of paths. Time required to check them all will be -
$time = number\space of\space paths\times time \space for\space each\space path$
$time=16777216×0.0001=1677.72 $
