I think when we speak of "putting out," "fire" is only countable. Examples of uncountable fire: There was fire everywhere. Fire from the roof spread to the living quarters.
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Vincent TeoThanks.Only d.
can I say,
(b) They are putting out the burning house.
(c) They are putting out the fire on the house / on the burning house.
(d) They are putting out the house fire.