Answer
Please see the work below.
Work Step by Step
We know that:
a. An acid and a base react together to produce water and a salt. Potassium iodide is a salt, and KOH and HI are bases.
$KOH+HI\rightarrow KI+H_2O$
b. We know that acids react with carbonates to produce carbon dioxide gas. HI and $K_2CO_3$ are an acid and a carbonate, respectively.
$2HI+K_2CO_3\rightarrow 2KI+CO_2+H_2O$
