1. **State the problem:** Solve the linear equation $$\frac{1}{3}x + 4 = 2$$. 2. **Isolate the variable term:** Subtract 4 from both sides to get $$\frac{1}{3}x + 4 - 4 = 2 - 4$$ which simplifies to $$\frac{1}{3}x = -2$$. 3. **Eliminate the fraction:** Multiply both sides by 3 to solve for $$x$$: $$3 \times \frac{1}{3}x = 3 \times (-2)$$ This gives $$\cancel{3} \times \frac{1}{\cancel{3}} x = -6$$, so $$x = -6$$. 4. **Check the solution:** Substitute $$x = -6$$ back into the original equation: $$\frac{1}{3}(-6) + 4 = -2 + 4 = 2$$ which is true. **Final answer:** $$x = -6$$.