The balanced chemical reaction is this:
2AgNO3(aq) + K2SO3(aq) -----> Ag2SO3(s) + 2KNO3(aq)
Next, we breakdown each compound into their ionic forms:
2Ag+(aq) + 2NO3-(aq) + 2K+(aq) + SO3 2-(aq) -----> Ag2SO3(s) + 2K+(aq) + 2NO3-(aq)
We inspect both sides of the reactions and cancel out terms that are present in both sides. These include: 2NO3-(aq), 2K+(aq)
Which leaves us with this:
2Ag+(aq) + SO3 2-(aq) -----> Ag2SO3(s)
