how many σ and π bonds are in this molecule?

Explanation:

Step1: Recall bond - type rules

Single bonds are $\sigma$ bonds. Double bonds have 1 $\sigma$ and 1 $\pi$ bond. Triple bonds have 1 $\sigma$ and 2 $\pi$ bonds.

Step2: Count $\sigma$ bonds

Count the single bonds first. There are 6 C - H single bonds, 3 C - C single bonds. The double bond has 1 $\sigma$ and the triple bond has 1 $\sigma$. So the number of $\sigma$ bonds is $6 + 3+1 + 1=11$.

Step3: Count $\pi$ bonds

The double bond has 1 $\pi$ bond and the triple bond has 2 $\pi$ bonds. So the number of $\pi$ bonds is $1 + 2=3$.

Answer:

There are 11 $\sigma$ bonds and 3 $\pi$ bonds.