The configurations at the two asymmetric centres (C-1 and C-6) in the bicyclo [4.4.0] decane, given below are A. 1R, 6R B. 1R, 6S C. 1S, 6S D. 1S, 6S

The correct answer is $\boxed{\text{C. 1S, 6S}}$.

To assign the configuration at each asymmetric center, we need to determine which group is coming out of the plane of the paper and which group is going into the plane of the paper. We can do this by using the Cahn-Ingold-Prelog (CIP) priority rules.

The CIP priority rules state that the following groups should be assigned the following priorities:

1. Atoms with higher atomic numbers have higher priority.
2. If two atoms have the same atomic number, the atom with more hydrogen atoms has higher priority.
3. If two atoms have the same atomic number and the same number of hydrogen atoms, the atom with the higher atomic number of the atom bonded to it has higher priority.

Once we have assigned the priorities to the groups around each asymmetric center, we can use the following rules to assign the configuration:

1. If the group with the lowest priority is going into the plane of the paper, the configuration is R.
2. If the group with the lowest priority is coming out of the plane of the paper, the configuration is S.

In the case of bicyclo [4.4.0] decane, the groups around C-1 are $\ce{CH3}$, $\ce{CH2}$, $\ce{CH2}$, and $\ce{CH2}$. The group with the lowest priority is $\ce{CH3}$, so it must be going into the plane of the paper. Therefore, the configuration at C-1 is S.

The groups around C-6 are $\ce{CH2}$, $\ce{CH2}$, $\ce{CH2}$, and $\ce{CH3}$. The group with the lowest priority is $\ce{CH3}$, so it must be going into the plane of the paper. Therefore, the configuration at C-6 is S.

Therefore, the configurations at the two asymmetric centers (C-1 and C-6) in the bicyclo [4.4.0] decane are $\boxed{\text{C. 1S, 6S}}$.