[bartleby]

A solution has a pH of 4.8.

1)  How do I calculate its hydrogen ion and hydroxide ion
concentrations?
2)  What's the answer?
3)  And, most importantly, what's the concept here?

[Borek]

3)  And, most importantly, what's the concept here?

pH definition, pH scale and check this page looking for water dissociation constant.

[hobaoe]

According to me any problems have solution and this is the solution for your problem
we know that pH =-log[H⁺]
 pH=4.8, therefore
-log[H⁺]=4.8
[H⁺]=10 ^-4.8
[OH^-]=(10 ^-14)/[H⁺]

the concept you can look up on the Internet(the source of info), Acid-Base

[Borek]

According to me any problems have solution

According to Gödel some problems don't have solutions:

http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems