In a Poisson distribution, the probability P of x successes is e^-m*m^x/x!, where m is the mean.
So if x=3, P=e^-m*m^3/3! and if x=4, P=e^-m*m^4/4!. If P(3)=(2/3)P(4), then m^3/6=(2/3)*m^4/24,
so m=3*24/(2*6)=6.
The standard deviation=sqrt(variance), and in a Poisson distribution, variance=mean,
so SD=sqrt(6)=2.45.