What happens if the Austrian forces under Francis Joseph defeat the French and Sardinian forces at the Battle of Solferino on June 24th, 1859?
Well, actually there were two interconnected battles, Solferino, where the French defeated the Austrians, and San Martino, where the Sardinians were engaged.
The Austrians were in a markedly worse state both strategically (having lost Lomborday) and tactically, but their opponents weren't that much better placed, so an Austrian victory is possible.
Ironically, the immediate aftermath is likely to be similar to OTL: Austria will have serious trouble trying to retake Lombardy, so, unless both parties go for attrition (think ACW in the Padan Plain) which I don't see happening, after a couple more fights a peace fairly similar to OTL armistice of Villafranca could be the immediate endgame.
The aftermath, however, will be very different. I don't see Garibaldi going to Sicily immadiately ITTL, but on the other hand, Cavour's diplomatic strategy would be seen as not working.
Even if Sardinia gets Lombardy, Italian unification isn't happening immediately, and that would discredit the House of Savoy as the main agent of it.