A person standing on a platform notes that a train travelling with...

The velocity of the train is given as $v = 0.6c$.

Substituting the speed of light $c = 3 \times 10^8 \text{ m/s}$:

$v = 0.6 \times 3 \times 10^8 \text{ m/s} = 1.8 \times 10^8 \text{ m/s}$

The time taken for the train to pass the person on the platform is $t = 1 \text{ s}$.

The length of the train as observed by the person is simply the distance the train travels in their frame of reference during this time interval.

$L = v \times t$

$L = 1.8 \times 10^8 \text{ m/s} \times 1 \text{ s} = 1.8 \times 10^8 \text{ m}$