Directions : Study the following information carefully and answer the given…

Concept: In these coded distance-direction puzzles, each statement 'X<symbol><number>Y' fixes point X relative to reference point Y along one compass axis: the symbol gives the direction (@ = north, % = south, # = east, $ = west) and the coded number converts to an actual distance by a fixed rule -- subtract 2 when the number is even, subtract 3 when it is odd. Chaining these statements plots every named point on one coordinate grid, so the direction between any two points is read off from the difference in their coordinates.

Application (place F at the origin since the question asks for W's direction with respect to F):

1. Decode the distances needed on the F-to-W chain: E$19F (19 is odd, distance 16) -> E is 16m west of F. C%11E (11 is odd, distance 8) -> C is 8m south of E. C$12B (12 is even, distance 10) -> C is 10m west of B. A%8B (8 is even, distance 6) -> A is 6m south of B. A$7R (7 is odd, distance 4) -> A is 4m west of R. R%14W (14 is even, distance 12) -> R is 12m south of W.

2. Set F = (0, 0). Then E = (-16, 0).

3. C is 8m further south of E: C = (-16, -8).

4. Since C is 10m west of B, B is 10m east of C: B = (-6, -8).

5. Since A is 6m south of B: A = (-6, -14).

6. Since A is 4m west of R, R is 4m east of A: R = (-2, -14).

7. Since R is 12m south of W, W is 12m north of R: W = (-2, -2).

8. Comparing W(-2, -2) with F(0, 0): W lies 2m west and 2m south of F.

Cross-check: Re-anchor the same chain at B instead of F as an independent check -- with B = (0, 0), working the same conditions gives F = (6, 8) and W = (4, 6). F minus W is (2, 2), so W is still 2 units west and 2 units south of F, confirming the direction is the same regardless of which point is chosen as the coordinate origin (the origin is only a bookkeeping choice; F is used as the primary reference here because the question asks for W's direction with respect to F).

So W is to the south-west of F.