Why 12 ? I think the Ti follow an exponential(lambda), and here, lambda=6
P(T1<1)=1-P(T1>1)=1-P(N(1)=0), because T1 is the time of first sighting. So if it's >1, it means that between 0 and 1, there have been no sighting.
And N(1) follows a Poisson distribution with parameter lambda.
Similarly, P(T1<2)=1-P(N(2)=0), and N(2) follows a Poisson distribution with parameter 2*lambda