Lithium-7 has 3 protons and 4 neutrons (mass number is 3 + 4 +7). You find this from the Nuclear Table. Its symbol is 73Li. If in the reaction one neutron is transferred from lithium to oxygen, the lithium nucleus will then have 3 protons and 3 neutrons. Its mass number will be 3 + 3 = 6, and it should be written 63Li. Since the proton number is the same, the nucleus is still called "lithium".
Similarly, the oxygen nucleus we start with is 168O, 8 protons and 8 neutrons, mass number 16. The neutron transferred from the lithium ends up in the oxygen nucleus, which then has 9 neutrons, mass number 8 + 9 = 17. Its symbol is 178O.
The reaction is written to show the initial nuclei, 73Li and 168O going to the final nuclei, 63Li and 178O.