Step 1: Understanding the Concept
The 14 Bravais lattices are distributed among 7 crystal systems.
Step 2: Count for each option
Cubic has 3 (primitive, body-centred, face-centred). Tetragonal has 2 (primitive, body-centred). Monoclinic has 2 (primitive, end-centred).
Step 3: Orthorhombic
Orthorhombic has 4: primitive, body-centred, face-centred and end-centred.
Final Answer:
The orthorhombic system has four types of unit cells.
\[ \boxed{\text{(B) }\text{Orthorhombic}} \]