Step 1: Concept
Terminal alkynes have acidic hydrogen, which reacts with strong bases like $NaNH_2$.
Step 2: Meaning
$NaNH_2$ (sodamide) reacts with terminal alkynes ($R-C \equiv C-H$) but not with internal alkynes ($R-C \equiv C-R$).
Step 3: Analysis
Ethyne, Propyne, and But-1-yne are terminal alkynes (have acidic H). But-2-yne is an internal alkyne (no acidic H).
Step 4: Conclusion
But-2-yne has no reaction with $NaNH_2$.
Final Answer: (C)