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**Hint:**Take into consideration the number of bonds each carbon is forming and whether they are $\sigma $-bonds or$\pi $-bonds. This will help you determine the hybridization of each carbon atom.

**Complete answer:**

First, let us identify and name the carbon atoms that are asked in the question:

${{C}^{1}}H\equiv {{C}^{2}}-{{C}^{3}}H={{C}^{4}}{{H}_{2}}$

We have to find the hybridization of the two carbons present in the middle.

Consider carbon number 2.

We can see that it is forming 1 $\sigma $-bond and 2 $\pi $-bonds with carbon number 1, and 1 $\sigma $-bond with carbon number 3. It does not form any bonds with a hydrogen atom.

Thus, it has 2 $\sigma $-bonds whose bond pairs we need to consider while calculating the hybridization of the atom. $\pi $-bonds are not considered while calculating the hybridization. As there are only 2 bond pairs involved, 2 hybridized orbitals are required to accommodate them. Thus, the hybridization of this carbon is $sp$.

Consider carbon number 3.

We can see that it is forming 1 $\sigma $-bond with carbon number 2, and 1 $\sigma $-bond and 1 $\pi $-bond with carbon number 4. It also forms 1 $\sigma $-bond with a hydrogen atom.

Now, to calculate the hybridization of this carbon, consider the number of $\sigma $-bonds present. We see that 3 $\sigma $-bonds are present and 3 hybridized orbitals are required to accommodate the 3 bond pairs. Thus, the hybridization of this carbon is $s{{p}^{2}}$.

**So, the correct answer is “Option B”.**

**Note:**Please be careful while calculating the number of $\sigma $-bonds that each of the carbon atoms forms with not only other carbon atoms but also the hydrogen atoms since they are not explicitly shown and you might miss them.

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