Odds in favor of an event = (no. of favorable event) / (no. of unfavorable event).
Let the probability that odd number comes up be x.
P(1) = P(3) = P(5) = x
P(2) = P(4) = P(6) = 2x.
Odds in favor of 6 showing up = (probability of showing 6 up) / (probability of not showing 6 up)
= $\frac{2x}{2x + 2x + x + x + x}$
= $\frac{2}{7}$