The conjugate acid : H₂CO₃
Further explanation
Given
Reaction
HCO₃− + H₂S → H₂CO₃ + HS−
Required
The conjugate acid
Solution
Bronsted-Lowry
Acid ⇒ H⁺ + conjugate base 
 Bases + H⁺⇒ conjugate acids 
Acid and conjugate base :  H₂S and HS−
Base and conjugate acid : HCO₃− and H₂CO₃
H₂S gives (H⁺), then the remaining acid is a conjugate base HS− 
HCO₃− receives (H +), then the conjugate acid H₂CO₃