Hybridization of ${\text{C}}_2$ and ${\text{C}}_3$ of ${\text{CH}}_3-\text{CH}=\text{C}=\text{CH}-{\text{CH}}_3$ are:

Let's number the carbon chain for the given allenic structure:
$$\stackrel{1}{C}{\text{H}}_3-\stackrel{2}{C}\text{H}=\stackrel{3}{C}=\stackrel{4}{C}\text{H}-\stackrel{5}{C}{\text{H}}_3$$

* Carbon-2 (${\text{C}}_2$) is involved in one double bond and two single bonds (forming $3$ $\sigma$ -bonds). Therefore, its hybridization is ${\text{sp}}^2$.
* Carbon-3 (${\text{C}}_3$) is involved in two double bonds (forming $2$ $\sigma$ -bonds). Therefore, its hybridization is $\text{sp}$.

Thus, the hybridization states are ${\text{sp}}^2$ and $\text{sp}$ respectively.