So here in this example question it states determine the number of protons, neutrons and electrons for the following cation. Now it's a cation because it possesses a positive charge, that positive charge being 3 plus. Now when looking at the other numbers we know that this 13 here represents our atomic number which uses the variable Z. Remember the atomic number gives us the number of protons, and because it's 13, that means we have 13 protons. That means that option D cannot be an answer because here we do not have 27 protons.
Next we have the number above the 13 in 27. Remember that is your mass number, which uses the variable A. Your mass number gives you the number of protons plus neutrons within the element or ion. From this information we know that the number of neutrons would equal A-Z. So it's the mass number minus the atomic number. So that would be 27-13=14 neutrons. So so far options B & C can be the only correct choices because in A we do not have 27 neutrons.
Now the charge is 3+. 3 plus means that you have lost electrons. It means you have lost three electrons. When aluminum is neutral, has no charge, it has an equal number of protons and electrons. OK, but now we've lost three electrons. So what does that mean? That means we have 10 electrons remaining. So the answer would have to be C here. And if you want to double check that, you can just say we have 13 protons and 10 electrons. So we know that would be +13+-10=+3, which would give us +3 as an answer. That proves that our charge should be plus three here.
So out of all the choices present, only option C gives the correct number for each of the subatomic particles.