First of all note:
68% is 0.68
2/3 is 0.66… ≈ 0.67
Secondly, you should review the facts about normal distribution.
This is the fact we use here:
A normal distribution has about 68% of its data within one standard deviation of the mean.
Here is the diagram, which shows how the mean (3.00 inches) and the values 2.75 inch, 3.25 inch relate according to the 68%-rule.
Each point represents the number of seed pods of a certain diameter.
The mean value is:
(diameter1 × number1 + diameter2 × number2 + … + diameterN × numberN) / (number1 + number2 + … + numberN)
The grey points represent all seed pods that have their diameters between 2.75 and 3.25. There are (numberK + … + numberM) of those seed pods.
The theorem says that (numberK + … + numberM)/(number1 + … + numberN) is about 68%.