Lizzie has a strange deck of 24 number cards that contains cards labeled 2 through 9 in three different colors (red, blue, and green).

Here's my best attempt...

a)

Possible sums of 10 =

2  3  5               

2  4  4              

2  6  2   

3  3  4        4 possibilities

For each of these  there are   3 possible colors for the first card, 2 for the second and 1 for the third = 3 * 2 * 1 =

6 possibilities

So.....

4 possbilities * 6 possibilities = 24 ways    

b)

Possible sums of 20

9 9 2        8  8  4         7  7  6       

9 8 3        8  7  5          

9 7 4        8  6  6

9 6 5 

So   again....we have 8 possibilities * 6 possibilities =    48  ways