Step 1: Picture the BCC cell.
A body-centred cubic cell has atoms at the 8 corners plus one atom right at the body centre.
Step 2: Recall sharing rules.
A corner atom is shared among 8 cells, so it contributes $\tfrac{1}{8}$ to one cell. A body-centre atom is inside one cell only, contributing $1$.
Step 3: Add up the corners.
$8 \text{ corners} \times \tfrac{1}{8} = 1$ atom from all corners together.
Step 4: Add the centre.
The single central atom adds $1$ more atom.
Step 5: Total the contributions.
$Z = 1 (\text{corners}) + 1 (\text{centre}) = 2$ atoms per unit cell.
Step 6: State the answer.
A BCC structure contains 2 particles per unit cell, which is option (4).
\[ \boxed{Z_{\text{BCC}} = 2} \]