What species is represented by the following information? #p^+ = 14#, #n^o = 12#, #e^(-) = 10#

Right from the start, you should know that the number of protons gives you the identity of the element.

Each element listed in the Periodic Table has a unique atomic number, i.e. each element has a unique number of protons located inside its nucleus.

So, your atom contains #14# protons inside its nucleus. Grab a periodic table and look for the element that has an atomic number equal to #14#.

You can thus say that you're dealing with silicon, #"Si"#.

Now, a neutral atom of silicon will have #14# protons inside its nucleus and #14# electrons surrounding its nucleus. In your case, the atom has #10# electrons surrounding the nucleus, which means that you're dealing with an ion.

More specifically, you're dealing with a positively charged ion, i.e. a cation. The charge of the cation is given by the difference between the number of protons and the number of electrons

#"charge" = "14 p"^(+) - "10 e"^(-) = 4+#

Therefore, you can say that you're dealing with a #"Si"^(4+)# cation.

Finally, you can use the number of neutrons to find the mass number, #A#, of the cation. As you know, the mass nubmer is equal to

#A = Z + n^(0)#

In your case, you have

#A = "14 p"^(+) + "12 n"^(0) = 26#

The tells you that you're dealing with the #4+# cation of a neutral silicon-26 atom. In isotope notation, this is written as

#""_14^26"Si"^(4+)#