Sample 1 has a half-life of 1 hrs, so after 6 hrs no of half lives elapsed = 6 half-lives...
Sample 2 has a half-life of 2 hrs, so after 6 hrs no of half lives elapsed = 3 half-lives...
After 6 half lives, the fraction of sample 1 left is 1/(26) = 1/64 ...
The fraction of sample 2 left is 1/(23) = 1/8....
Since sample 1/sample 2 started out at 2/3, the ratio of sample 1/sample 2 at 6 hrs = [(1/64) / (1/8)]* [2/3] = [1/8]*[2/3] = 1/12...
Required ratio is 1:12 [Option #2 is the answer]