A man is facing West. He turns 45 degrees in the clockwise direction, then…

Concept:

In a direction test, the eight compass positions -- North, North-East, East, South-East, South, South-West, West, North-West -- are spaced 45 degrees apart around the circle. A clockwise turn moves forward through this list (North to North-East to East and so on back to North); an anti-clockwise turn moves backward through the same list. To find the final facing direction after several turns, track the position reached after EACH turn in order, always turning from the position reached at the end of the previous turn -- never restarting from the original direction.

Step-by-step application:

1. Start: facing West.

2. Turn 45 degrees clockwise from West -- one 45-degree step forward in the clockwise list -- reaches North-West.

3. Turn 180 degrees clockwise from North-West -- four 45-degree steps forward (North-West, North, North-East, East, South-East) -- reaches South-East.

4. Turn 270 degrees anti-clockwise from South-East -- six 45-degree steps backward (South-East, East, North-East, North, North-West, West, South-West) -- reaches South-West.

Cross-check:

As an independent check, combine the three turns algebraically with clockwise taken as positive: +45 degrees + 180 degrees - 270 degrees (anti-clockwise is the opposite sense) = -45 degrees, i.e. a net 45-degree anti-clockwise shift from the original West-facing direction. Moving one 45-degree step anti-clockwise from West also lands on South-West, confirming the step-by-step result.

Final direction: South-West.