1. **State the problem:** Find the limit $$\lim_{(x,y) \to (2,2)} \frac{x - y}{x^4 - y^4}.$$\n\n2. **Recall the formula and important rules:** The expression involves a difference quotient with a difference of fourth powers in the denominator. We can factor the denominator using the difference of powers formula: $$a^4 - b^4 = (a - b)(a^3 + a^2b + ab^2 + b^3).$$\n\n3. **Apply factorization:**\n$$\frac{x - y}{x^4 - y^4} = \frac{x - y}{(x - y)(x^3 + x^2y + xy^2 + y^3)}.$$\n\n4. **Cancel common factors:**\n$$\frac{\cancel{x - y}}{\cancel{x - y}(x^3 + x^2y + xy^2 + y^3)} = \frac{1}{x^3 + x^2y + xy^2 + y^3}.$$\n\n5. **Evaluate the limit by substituting $(x,y) = (2,2)$:**\n$$\frac{1}{2^3 + 2^2 \cdot 2 + 2 \cdot 2^2 + 2^3} = \frac{1}{8 + 8 + 8 + 8} = \frac{1}{32}.$$\n\n**Final answer:** $$\boxed{\frac{1}{32}}.$$