I was given a list of 14 different solutions, and

My homework question asks which of the solutions exhibit the common-ion effect and which ones are buffers?
But, how would I be able to tell???

A common ion is just what you think it is. For example, a solution of NaNO3 and KNo3 has a common ion; i.e., the NO3^-. AgCl saturated solution with AgBr (or NaCl)O has a common ion.

A buffer basically is a weak acid and its salt (such as acetic acid and sodium acetate) or a weak base and its salt (such as NH3 and NH4Cl.