For this type of problem you need to find the least mole given in problem to coeffiecent (from the balanced equation) to figure out which one is the limiting reagant or reactant. The limiting reactant will be the one whose number is lower.
For example let us first look at the equation and make sure that it is balanced:
2 AgNO3 + Cu → Cu(NO3)2 + 2 Ag
You have 2 silvers Ag on each side
2 Nitrate ions on each side
1 Copper Cu on each side
So this is indeed a balanced equation.
Now for each species on the reactant side find the mole coeffecient ratio, which ever one is lowest is the limiting reagant/reactant:
For silver Nitrate AgNO3 in the problem you are given 3 moles, the number in front in the balanced equation is 2 so 3/2 is 1.5
For copper Cu, 2 is given in the problem, 1 is the coeffecient in front in the balanced equation so 2/1 = 2
The limiting reagant/reactant is Silver Nitrate AgNO3 it has the smaller number with 1.5.
So now proceed the reaction with this species to know how many moles of Cu(NO3)2 you wil have.
If 2 moles of AgNO3 -----> 1 mol of Cu(NO3)2:
Then 3 moles of AgNO3 ------> ? mol of Cu(NO3)2
set up a ratio, cross multiply and solve for the unknown:
2AgNO3 = 1Cu(NO3)2
___________________ ----------------> 2 = 1
3AgNO3 = XCu(NO3)2 ---------
3 = X
2X = 3, X=2/3
So your X value will be equal to 2/3 or .66666666 repeating in terms of moles for Copper Nitrate or Cu(NO3)2
so you will have 0.666 moles or 2/3 moles of Cu(NO3)2, Starting with 3 moles of AgNO3