what is the ph of a solution in which 250.0 ml of .200 M HNO3 is added to 280.0 ml of .150 Ba(OH )

2HNO3 + Ba(OH)2 ==> 2H2O + Ba(NO3)2

mols HNO3 = M x L = ?
Use the coefficients to convert mols HNO3 to mols Ba(NO3)2.
mols Ba(OH)2 = M x L = ?
Convert mols Ba(OH)2 to mols Ba(NO3)2.
It is likely you will obtain two different numbers for mols Ba(NO3)2 so one of them must be wrong. The correct value in limiting reagent problems is ALWAYS the smaller value and the reagent producing that number is the limiting reagent.
The non-limiting reagent will be the one in excess. Use the coefficients to determiner how much of the excess reagent remains after the reaction and use it and pH = -log(H^+) or pOH = -log(OH^-) to determine pH. If you use pOH, then pH + pOH = pKw = 14 and you can convert to pH from pOH. Post your work if you get stuck.