Let's solve the system of equations given by x - y = 2 and \(x^2 - y^2 = 8\). From the first equation, we can solve for x in terms of y: x = y + 2. Substituting this expression for x into the second equation, we get \((y + 2)^2 - y^2 = 8\), which simplifies to \(y^2 + 4y + 4 - y^2 = 8\), or \(4y + 4 = 8\). Solving for y, we get y = 1. Substituting this value of y into the first equation, we get x = y + 2 = 1 + 2 = 3.

Therefore, the solution to the system of equations is (x, y) = **(3, 1)**, which means the correct answer is **B. (3, 1)**.