Treatment of buta-1,3-diyne with NaNH_2 ( 2 equivalents), followed...

Buta-1,3-diyne ($HC \equiv C - C \equiv CH$) reacts with $2$ equivalents of $\text{NaNH}_2$ to undergo double deprotonation, forming the acetylide dianion:

$HC \equiv C - C \equiv CH + 2\text{NaNH}_2 \rightarrow \ ^\ominus C \equiv C - C \equiv C ^\ominus + 2\text{NH}_3$

This dianion acts as a strong nucleophile and undergoes an $S_N2$ reaction with the primary allylic halide, $trans$-$\text{CH}_3\text{-CH=CH-CH}_2\text{-Br}$ (excess ensures both sides react):

$^\ominus C \equiv C - C \equiv C ^\ominus + 2 \text{CH}_3\text{-CH=CH-CH}_2\text{-Br} \rightarrow \text{CH}_3\text{-CH=CH-CH}_2 - C \equiv C - C \equiv C - \text{CH}_2\text{-CH=CH-CH}_3$

In the major product $\textbf{X}$, the central diyne unit consists of four $sp$ hybridized carbon atoms. The geometry around $sp$ hybridized carbons is linear (bond angle $180^\circ$).

The two $sp^3$ hybridized $-\text{CH}_2-$ carbons attached directly to the $sp$ carbons also lie on this same linear axis. Thus, the sequence of collinear carbon atoms is:

$-\text{CH}_2 - C \equiv C - C \equiv C - \text{CH}_2-$

The carbon atoms beyond the $-\text{CH}_2-$ groups are attached at a tetrahedral angle ($\sim 109.5^\circ$) and are not collinear with the central axis.

Therefore, the maximum number of collinear carbon atoms in $\textbf{X}$ is $6$.

Answer: $6$