Assume that the business makes a profit with probability 0.6 in the first year. for each year thereafter, the business makes a profit with probability 0.6 if it made a profit in the previous year, and with probability 0.4 if it did not make a profit in the previous year.

It profits in years can be one and two but not three or one and three but not two or not one, but two and three. 

"Or" means to add, so we just need to figure out the things in the statement mentioned and add them. 

If we follow the map they laid out carefully, the first set is 0.6 x 0.6 x 0.3
The second set is 0.6 x 0.4 x 0.4. 
The third is 0.6 x 0.4 x 0.6. 

So these are 0.108+0.096+0.144 = 0.348.

Hope this helps.