The reaction is:

^{7}_{3}Li + ^{14}_{7}N --> X + ^{17}_{8}O.

In any reaction (except beta decay) the total number of protons is the same before and after the reaction. Also the total number of neutrons is the same before and after. It follows that the total of the mass numbers before the reaction is the same as after the reaction. Therefore, we can figure out the proton number and the mass number of X.

The total proton number on the left is 3 + 7 = 10. The proton number of the oxygen on the right is 8, so the proton number of X must 10 - 8 = 2. The total mass number on the left is 21, so the mass number of X must be 21 - 17 = 4. The element with atomic number 2 is helium. So X must be ^{4}_{2}He.