1. **Problem statement:** Find the number 6 units backwards from 3 on the number line. 2. **Formula and rule:** Moving backwards on the number line means subtracting the number of units from the starting point. So, if you start at $x$ and move $n$ units backwards, the new position is given by: $$x - n$$ 3. **Apply the formula:** Here, $x = 3$ and $n = 6$, so: $$3 - 6 = -3$$ 4. **Interpretation:** The number 6 units backwards from 3 is $-3$. 5. **Summary:** On the number line, moving backwards means subtracting units. Starting at 3 and moving 6 units backwards lands you at $-3$. **Final answer:** $-3$