Step 1: Analyzing the paper fold patterns.
We need to check how the red line connects in each option when the paper is folded into a cube. The cube must have a continuous path for the red line.
Step 2: Folding each paper piece.
- Option (A): The red line does not form a continuous loop when folded.
- Option (B): When folded into a cube, the red line forms a continuous loop.
- Option (C): The red line does not form a continuous loop.
- Option (D): The red line does not form a continuous loop.
\[
\boxed{(B)}
\]