How to Say "extinguishing" in Spanish
The Spanish word for “extinguishing” is “extinción” — B2 level.

Examples
Los bomberos trabajan en la extinción del incendio forestal.
The firefighters are working on extinguishing the forest fire.
La extinción de la deuda se completará el próximo mes.
The termination of the debt will be completed next month.
El contrato prevé varias causas de extinción.
The contract provides for several grounds for termination.
Action vs Result
In this context, the word describes the process of putting something out (like a fire) or the legal act of ending something.
Confusing with 'extinguidor'
Mistake: “Usar 'extinción' para referirse al objeto que apaga el fuego.”
Correction: The object is an 'extintor' (fire extinguisher); 'extinción' is the act of putting it out.
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