1. The problem is to simplify the expression $$\frac{4}{4 + \sqrt{14}}$$. 2. To simplify a fraction with a surd in the denominator, we multiply numerator and denominator by the conjugate of the denominator to rationalize it. The conjugate of $$4 + \sqrt{14}$$ is $$4 - \sqrt{14}$$. 3. Multiply numerator and denominator by $$4 - \sqrt{14}$$: $$\frac{4}{4 + \sqrt{14}} \times \frac{4 - \sqrt{14}}{4 - \sqrt{14}} = \frac{4(4 - \sqrt{14})}{(4 + \sqrt{14})(4 - \sqrt{14})}$$ 4. Simplify the denominator using the difference of squares formula: $$ (4 + \sqrt{14})(4 - \sqrt{14}) = 4^2 - (\sqrt{14})^2 = 16 - 14 = 2 $$ 5. So the expression becomes: $$ \frac{4(4 - \sqrt{14})}{2} $$ 6. Distribute the 4 in the numerator: $$ \frac{16 - 4\sqrt{14}}{2} $$ 7. Simplify the fraction by dividing numerator and denominator by 2: $$ \frac{\cancel{16}^8 - \cancel{4}^2\sqrt{14}}{\cancel{2}^1} = 8 - 2\sqrt{14} $$ 8. Therefore, the simplified form is $$8 - 2\sqrt{14}$$. 9. Comparing with the options, the answer is (b) $$8 - 2 \sqrt{14}$$.