To find the average rainfall per day, first calculate the total rainfall in the week:
\[
\text{Total rainfall} = 4 + 5 + 12 + 3 + 6 + 8 + 4 = 42 \, \text{cm}
\]
Now, divide the total rainfall by the number of days in a week (7 days):
\[
\text{Average rainfall per day} = \frac{42}{7} = 6 \, \text{cm}
\]
Thus, the correct answer is option (3).