Write the structure of $\mathrm{Mn_2O_7}$

$\mathrm{Mn_2O_7}$ is the anhydride of permanganic acid and has the structure:

$\mathrm{O_3Mn - O - MnO_3}$

That means there are:

• one bridging oxygen atom between the two Mn atoms
• three terminal oxygens attached to each Mn atom

Count oxidation state and bonding idea

Each Mn is in oxidation state $+7$.

In this structure, for each Mn:

• 1 oxygen is a bridging oxygen: $\mathrm{Mn-O-Mn}$
• 3 oxygens are terminal and represented as $\mathrm{Mn=O}$

Count total $\mathrm{Mn=O}$ bonds

Since each Mn has 3 terminal $\mathrm{Mn=O}$ bonds, and there are 2 Mn atoms:

$\text{Total } \mathrm{Mn=O} \text{ bonds} = 2 \times 3 = 6$

Match with options

$6$

So the correct option is C.