1. Interpret the name and write the structure

The parent chain is hex-4-ynoic acid:

• 6 carbon chain
• carboxylic acid carbon is carbon-1
• triple bond between carbon-4 and carbon-5
• 2-oxo means a keto group at carbon-2

So the structure is:

$\mathrm{HOOC-CO-CH_2-C\equiv C-CH_3}$

Numbering:

$\mathrm{C_1(=O)OH - C_2(=O) - C_3H_2 - C_4\equiv C_5 - C_6H_3}$

2. Count the $\sigma$ bonds

Count each connected pair of atoms once for one $\sigma$ bond.

(a) Between heavy atoms

• $\mathrm{C_1-O}$ in $\mathrm{C_1=O}$ : $1\sigma$
• $\mathrm{C_1-O}$ in $\mathrm{O-H}$ group : $1\sigma$
• $\mathrm{C_1-C_2}$ : $1\sigma$
• $\mathrm{C_2-O}$ in keto group : $1\sigma$
• $\mathrm{C_2-C_3}$ : $1\sigma$
• $\mathrm{C_3-C_4}$ : $1\sigma$
• $\mathrm{C_4\equiv C_5}$ : $1\sigma$
• $\mathrm{C_5-C_6}$ : $1\sigma$

Total heavy-atom $\sigma$ bonds = $8$

(b) Bonds involving hydrogen

• $\mathrm{O-H}$ : $1\sigma$
• $\mathrm{C_3H_2}$ : $2\sigma$
• $\mathrm{C_6H_3}$ : $3\sigma$

Total $\sigma$ bonds with H = $1+2+3=6$

Therefore,

$\text{Total } \sigma = 8+6=14$

3. Count the $\pi$ bonds

• Carboxylic acid carbonyl $\mathrm{C_1=O}$ gives $1\pi$
• Keto group at $\mathrm{C_2=O}$ gives $1\pi$
• Triple bond $\mathrm{C_4\equiv C_5}$ gives $2\pi$

So,

$\text{Total } \pi = 1+1+2=4$

4. Total number of $\sigma$ and $\pi$ bonds

$\text{Total bonds} = 14+4=18$

5. Compare with stored answer

Derived answer = $18$

Stored correct answer = $18$

They match.