To solve \( 6(82) \) using place value and the distributive property, we start by breaking down \( 82 \) into \( 80 + 2 \):
\[ 6(82) = 6(80 + 2) \]
Next, we can use the distributive property:
\[ 6(80 + 2) = 6 \times 80 + 6 \times 2 \]
Now, we calculate each part:
- \( 6 \times 80 = 480 \)
- \( 6 \times 2 = 12 \)
Now we add these two results together:
\[ 480 + 12 = 492 \]
Thus, the value of \( 6(82) \) is:
\[ \boxed{492} \]