Use the known structure of $Co_2(CO)_8$

Dicobalt octacarbonyl exists in the bridged form in which:

• there are two bridging $CO$ ligands,
• the remaining six $CO$ ligands are terminal,
• and there is one $Co-Co$ bond.

Electron-count check

Each cobalt in $Co_2(CO)_8$ is a metal center bonded to:

• $3$ terminal $CO$ ligands,
• $2$ bridging $CO$ ligands (shared),
• $1$ $Co-Co$ bond.

For one Co atom:

• Co contributes $9$ electrons,
• $3$ terminal $CO$ donate $3 \times 2 = 6$ electrons,
• $2$ bridging $CO$ contribute $1$ electron each to one Co in the neutral counting picture, so $2$ electrons,
• one $Co-Co$ bond contributes $1$ electron.

Total: $9+6+2+1=18$

So each Co attains the stable $18$-electron configuration, which supports the structure having 2 bridging carbonyls and 1 metal-metal bond.

Check the options

• A: $2$ and $0$ → incorrect, because the bridged structure has a $Co-Co$ bond.
• B: $0$ and $2$ → incorrect, no such structure with two $Co-Co$ bonds.
• C: $4$ and $0$ → incorrect.
• D: $2$ and $1$ → correct.

Final answer

The number of bridging $CO$ ligands and $Co-Co$ bonds in $Co_2(CO)_8$ are: $\boxed{2 \text{ and } 1}$