Concept:
For compounds containing both double and triple bonds:
• Choose the longest chain containing all multiple bonds.
• Number the chain to give the lowest set of locants.
• If a tie occurs, double bonds receive lower numbers than triple bonds.
• Write ``en'' before ``yne'' in the name.
Step 1: Determine the parent chain.
The compound contains eight carbon atoms.
\[\begin{aligned}
\text{Parent chain} = \text{Octa}
\end{aligned}\]
Step 2: Locate the multiple bonds.
Numbering from the left gives
\[\begin{aligned}
\text{Triple bond at }2
\end{aligned}\]
and
\[\begin{aligned}
\text{Double bonds at }4,6
\end{aligned}\]
Numbering from the right gives
\[\begin{aligned}
\text{Double bonds at }2,4
\end{aligned}\]
and
\[\begin{aligned}
\text{Triple bond at }6
\end{aligned}\]
Step 3: Apply IUPAC priority rule.
Both numberings give the same set of locants \((2,4,6)\).
In such a tie, double bonds receive lower numbers.
Hence the preferred numbering is
\[\begin{aligned}
\text{Double bonds: }2,4
\end{aligned}\]
\[\begin{aligned}
\text{Triple bond: }6
\end{aligned}\]
Step 4: Write the IUPAC name.
\[\begin{aligned}
\boxed{\text{Octa-2,4-dien-6-yne}}
\end{aligned}\]
This corresponds to option (B).