I solved this problem by following the hint given.
1)If charlie picks the green die, Alison would pick the blue die
2)If charlie picks the red die, Alison would pick the green die
3)If charlie picks the blue die, Alison would pick the red die
Reasons for this;
For any colour charlie picks Alison will always pick a die which gives her a higher chance of rolling the highest number. e.g. when charlie picks the green die, his only possible rolls are (2, 4 , 9) therefore for Alison to beat this she will have to pick the blue die since this gives her a higher advantage over charlie.Since the blue die have possibilities (3, 5, 7)
From this we can deduct that since 2<3, 4<5, and 9>7
the probability of Alison rolling a higher number in this case is 2 out of 3 possibilities = two-third which is either 3 or 5
the probability of Charlie rolling a higher number in this case is 1 out of 3 possiblities = one-third which is 9.
The same solution goes for suggestion (2) and (3).
In conclusion it is a good idea if Alison allows charlie to go first.