Step 1: Analyzing the self-portraits.
- P is a self-portrait of Pablo Picasso, known for his distinct cubist style.
- Q is a self-portrait of Rembrandt, known for his realistic portrayal.
- R is a self-portrait of Vincent van Gogh, known for his expressive brushwork.
- S is a self-portrait of Paul Gauguin, known for his bold and vibrant colors.
Step 2: Matching the portraits to the artists.
- Option (C) correctly matches the portraits with their respective artists based on the style and characteristics of each painting.
\[
\boxed{(C)}
\]