Answer
The space that should be left between the track sections is $8.78~mm$
Work Step by Step
We can find the increase in length of each section of steel track when it is heated:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(40.0~K)(18.30~m)$
$\Delta L = 8780\times 10^{-6}~m$
$\Delta L = 8.78\times 10^{-3}~m$
$\Delta L = 8.78~mm$
Since we can assume that each section expands by half of this distance in each direction, the space that should be left between the track sections is $8.78~mm$
