If i understand the question correctly, i think that solution is this:

Y......................0..........1..........2.... ......Sum

p(y)..................1/7.......3/7.......3/7........1

y.P(y)................0..........3/7.......6/7........9/7

...81/49.....42/49....21/49

So, probability that the value of Y falls within 2 standard deviations is

Y=1 and Y=2, P(Y=1)+P(Y=2)=3/7+3/7=6/7