1. **Problem statement:** A number when divided by 30 leaves a remainder of 8. We need to find what number should be added to this number to make it a multiple of 6. 2. **Understanding the problem:** Let the number be $n$. When divided by 30, remainder is 8, so: $$n = 30k + 8$$ for some integer $k$. 3. **Goal:** Find a number $x$ such that: $$n + x$$ is divisible by 6, i.e., $$n + x \equiv 0 \pmod{6}$$ 4. **Substitute $n$:** $$30k + 8 + x \equiv 0 \pmod{6}$$ 5. **Simplify modulo 6:** Since $30k$ is divisible by 6 (because 30 is divisible by 6), $$30k \equiv 0 \pmod{6}$$ So, $$8 + x \equiv 0 \pmod{6}$$ 6. **Reduce 8 modulo 6:** $$8 \equiv 2 \pmod{6}$$ So, $$2 + x \equiv 0 \pmod{6}$$ 7. **Solve for $x$:** $$x \equiv -2 \equiv 4 \pmod{6}$$ 8. **Answer:** The smallest positive number to add is $4$. **Final answer:** $4$