Write the known structure of $[Co_2(CO)_8]$

The dicobalt octacarbonyl complex exists in the common bridged form with:

• one $Co-Co$ bond
• two bridging $CO$ ligands
• remaining $CO$ ligands as terminal

Count the number of terminal $CO$ ligands

Total carbonyl ligands $= 8$

Bridging carbonyl ligands $= 2$

Therefore terminal carbonyl ligands: $Y = 8 - 2 = 6$

Count the number of $Co-Co$ bonds

In $[Co_2(CO)_8]$, there is: $X = 1$

Compute $X+Y$

$X + Y = 1 + 6 = 7$

Final answer

$\boxed{7}$

Comparison with stored correct answer

Stored correct answer $= 7$

Our derived answer also $= 7$, so they agree.