This would be a double replacement reactions so the metals will switch places and you balance based on the charges: Li(+1), Ag (+1), SO4(-2), NO3(-1)
No we look at our solubility rules are either of the products insoluble?
Ag2SO4 is insoluble so will be a solid, but LiNO3 is aqueous
Then we balance our reaction, do we have any with different amounts on each side? How do we fix it?
1 Ag on left, 2 on right
2 Li on left, 1 on right
Since with both of those changes we doubled our NO3 we are sill balanced on our anions so we are good to continue.
Break into complete ionic equation but writing (aq) compounds as their separate ions
If we look Li+ and NO3- are in solution on both sides so nothing is changing for them, they are spectator ions because they just "watch" the reaction so we cut them out.
We are left with our Net Ionic equation showing only what is actually reacting.