Introduction:
In this problem, we are given two solutions - a strong acid solution with a pH of 2 and a buffer solution with a pH of 4. We need to determine the pH of the resulting solution when these two solutions are mixed together.

Understanding pH:
pH is a measure of the acidity or alkalinity of a solution. It is defined as the negative logarithm (base 10) of the concentration of hydrogen ions (H+) in a solution. A lower pH value indicates a higher concentration of H+ ions, making the solution more acidic.

Properties of a Strong Acid:
A strong acid is one that completely dissociates in water, releasing all of its H+ ions. Since the pH of the strong acid solution is given as 2, it means that the concentration of H+ ions in this solution is 10^(-2) M.

Properties of a Buffer Solution:
A buffer solution is a mixture of a weak acid (HA) and its conjugate base (A-). It resists changes in pH when small amounts of acid or base are added to it. The pH of a buffer solution is determined by the equilibrium between the weak acid and its conjugate base.

Mixing the Solutions:
When the strong acid solution (pH = 2) is mixed with the buffer solution (pH = 4), the strong acid will dissociate and contribute more H+ ions to the solution. These H+ ions will react with the weak acid in the buffer solution, shifting the equilibrium towards the formation of more conjugate base.

Calculating the pH of the Resulting Solution:
To calculate the pH of the resulting solution, we need to consider the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the weak acid and the ratio of the concentrations of the weak acid and its conjugate base.

The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])

In this case, the pH of the resulting solution will be closer to the pKa of the weak acid in the buffer solution (as the strong acid concentration is much smaller compared to the buffer solution). Let's assume the pKa of the weak acid is X.

Using the Henderson-Hasselbalch equation, we can write:
pH = X + log([A-]/[HA])

Since the concentrations of [A-] and [HA] are not given, we cannot calculate the exact pH value. However, we can conclude that the pH of the resulting solution will be slightly lower than the pH of the buffer solution (pH 4) due to the addition of the strong acid solution.

Summary:
When a strong acid solution with pH 2 is mixed with a buffer solution of pH 4, the resulting solution will have a pH slightly lower than 4. The exact pH value depends on the pKa of the weak acid in the buffer solution and the ratio of the concentrations of the weak acid and its conjugate base. The Henderson-Hasselbalch equation can be used to calculate the pH of the resulting solution, but without the specific concentrations, we can only determine that the pH will be slightly lower than the initial pH of the buffer solution.