Answer
This is an acid-base reaction:
Acid: $H_2CO_3 (H_2O + CO_2)$
Base: $NH_3$
Work Step by Step
** Notice, the carbon dioxide and water are capable of forming carbonic acid:
$CO_2 + H_2O -- \gt H_2CO_3$
And, when we add a base, like ammonia, this happens:
$NH_3 + H_2CO_3 -- \gt NH_4HCO_3$
** The carbonic acid gave an $H^+$ to the ammonia, so, this is an acid-base reaction.