If a speaker gives a sound intensity of 10−6w/m2 at a certain point, what is the sound intensity level β at that point?

Start with basic concept that you have the same amount of watts it's just how far away you are dictates the watts/meter squared (per area). As the distance from the object is increased, the area increases as distance squared (think of a sphere of increasing radius, as you increase the radius, the surface area increases as r^2, double radius, you get 4 times area, triple radius, 9 times area, and so forth). so safe from acoustical effects (reflections off walls, etc) as you increase the distance from a speaker, the sound will decrease by a factor of the distance squared, as before 2x distance =1/4 power, 3x distance =1/9 power. 

so the only thing left out of your questions is what distance from speaker is the level at 10^-6 W/m^2 and what distance is point B from the speaker, and apply the 1/distance^2 principle. 

The power at point B (PB) is the following: 

power at given power level (we will call this point A or PA). 

PB=PA*(DA/DB)^2 

Where PB is power level at PB (in W/m^2) 
PA=power at point A or 10^-6 W/m^2 
DA=distance from speaker to point A 
DB=distance from speaker to point B. 

The answer is a 0.64 volts