The first thing you do is write out what you know with the information given on the problem:
Zn + Pb(NO3)2 --> Zn(NO3)2 + Pb
Since you know you're dealing with lead (II), then you know you need 2 nitrate ions to balance the overall charge of the compound, because the charge of a nitrate ion is always -1. I don't know what the problem says, but I will assume we're also dealing with zinc (II). Now you count the number of atoms of each element on both sides of the equation. If they are already equal, as is the case with the above reaction, then you are done. However, if there was a different number of atoms of the same element on either side of the equation, then you would have to place coefficients in front of the element or compound until both sides have the same number of atoms of each element.
Also, don't forget to include state symbols if the problem requires it. (e.g., (s), (aq))
Zn + Pb(NO3)2 --> Zn(NO3)2 + Pb
Since you know you're dealing with lead (II), then you know you need 2 nitrate ions to balance the overall charge of the compound, because the charge of a nitrate ion is always -1. I don't know what the problem says, but I will assume we're also dealing with zinc (II). Now you count the number of atoms of each element on both sides of the equation. If they are already equal, as is the case with the above reaction, then you are done. However, if there was a different number of atoms of the same element on either side of the equation, then you would have to place coefficients in front of the element or compound until both sides have the same number of atoms of each element.
Also, don't forget to include state symbols if the problem requires it. (e.g., (s), (aq))
