A solution of barium chromate is prepared by dissolving 6.3 x 10-3 g of this yellow solid in 1.00 L of hot water. Will solid barium chromate precipitate upon cooling to 25°C? Proof?

You want to compare Qsp to Ksp (at 25o C.)
Ag2CrO4(s) ==>2Ag^+ + CrO4^=

Ksp = (Ag^+)^2(CrO4^=) = ?? Look it up in your text or notes (at 25 degrees C).
6.3E-3g/molar mass Ag2CrO4 = mols Ag2CrO4 in 1. Lets call this value x molar.
2x then will be Ag^+ and x will be CrO4^=. Plug those values in and multiply them together. Don't forget to square the Ag^+. This will be Qsp See how Ksp compares with Qsp. Ksp CAN'T be exceeded; therefore, if Qsp is larger, a ppt will occur. If Qsp is smaller, no ppt.
Proof?? You can perform the experiment in the lab but be warned. Ksp calculation IS AT EQUILIBRIUM. What happens if you cool the silver chromate to 25 and no ppt occurs but one, by the calculations, SHOULD. What about the possibility of a supersaturated solution? Then what?