An atom is composed of electrons, protons, and neutrons. The electrons are in outer rings (and weigh very little), the neutrons and protons are in the nucleus and together they have most of the mass of the atom. The neutron is neutrally charged, the proton is positively charged and the electron is negatively charged. Since the atom is neutral electrically, the NUMBER of electrons always equals the NUMBER of protons. Here is how all that is put together.
The number of protons in an atom is called the atomic number. Look at the periodic table. Each element has an atomic number. Atomic numbers start at 1 and go to something like 118 or so. That will automatically tell you the number of protons (and incidentally, the number of electrons,too).
The number of protons PLUS the number of neutrons is called the MASS NUMBER of the element.
SO, to your problem. If the element has 7 protons, just look on the periodic chart, find element number 7 and write its symbol.
Since the mass is made up of the number of protons and the number of neutrons, the MASS NUMBER is the total. Your problem tells you the mass number is 15.
So write the symbol for element number 7. On the lower left side write that number as a subscript. On the upper left side write the mass number as a superscript.
Example. Write the symbol for an atom with 8 protons and 9 neutrons. So I will find element #8 which is oxygen, and knowing its mass number of 17 I will write
I hope this helps clear things up for you. And I hope I addressed what you really don't understand about "this whole protons and neutrons thing."
These boards don't have good spacing but the above sub8 super17 O was the best I could do. You understand that the 8 should go directly under the 17. The 17 is a superscript. The 8 is a subscript. The O is regular type but I put everything in bold face type to make it show up a little better.