Given Information:
P, Q, R, S, T, U, V and W are sitting around a circle facing the center.
P is second to the right of T who is the neighbor of R and V.
S is not the neighbor of P.
V is the neighbor of U.
Q is not between S and W.
W is not between U and S.
We need to find the two options that are not neighbors.

Arranging the given information:
Let us first arrange the given information in a tabular form for better visualization.

|---------------------------|---------------------------|
| Clockwise Direction | Anti-Clockwise Direction |
|---------------------------|---------------------------|
| T | V |
| P | R |
| R | T |
| V | P |
| | U |
| S | Q |
| U | W |
| Q | S |
|---------------------------|---------------------------|

From the above table, we can infer the following:
- T and P are adjacent and R and V are adjacent.
- S cannot be the neighbor of P, so it can be either U or Q.
- V is the neighbor of U, so V cannot be adjacent to Q or W.
- Similarly, U is not adjacent to Q or W.
- Also, Q is not between S and W, so it can be either U or P.
- W is not between U and S, so it can be either V or T.

Using the above inferences, we can now answer the question.

Solution:
To find the two options that are not neighbors, we need to check all possible pairs of options:
- UV: V cannot be adjacent to Q or W. So, UV are neighbors.
- RP: R and V are adjacent, so RP are not neighbors.
- QW: Q can be adjacent to P or U. So, QW can be neighbors or not. We need to check further.
- If Q is adjacent to P, then W can be adjacent to T or U. So, QW can be neighbors.
- If Q is adjacent to U, then W can be adjacent to V or T. So, QW can be neighbors.
- Hence, QW can be neighbors or not neighbors.
- RV: R and V are adjacent, so RV are not neighbors.

Therefore, the two options that are not neighbors are RP and RV, which is option (d).

Note: It is important to arrange the given information in a tabular form or any other suitable form to visualize the problem better and to avoid confusion.