1. **State the problem:** We need to find the value of $K$ given the equation $$\frac{K + K}{K} = 6.$$\n\n2. **Write the formula and simplify:** The numerator is $K + K$, which simplifies to $2K$. So the equation becomes $$\frac{2K}{K} = 6.$$\n\n3. **Simplify the fraction:** Since $K \neq 0$, we can cancel $K$ in numerator and denominator: $$\frac{\cancel{2K}}{\cancel{K}} = 2 = 6.$$\n\n4. **Analyze the result:** We get $2 = 6$, which is a contradiction. This means there is no value of $K$ (except possibly $K=0$) that satisfies the equation.\n\n5. **Check $K=0$:** Substituting $K=0$ makes the denominator zero, which is undefined.\n\n**Final answer:** There is no value of $K$ that satisfies the equation $$\frac{K + K}{K} = 6.$$