Let \( x \) represent the number of seashells Lucy has. According to the problem, Daisy has 6 more than three times the number of seashells Lucy has. We can express this relationship with the equation:
\[ D = 3x + 6 \]
We know Daisy has 36 seashells, so we can substitute \( D \) with 36 in the equation:
\[ 36 = 3x + 6 \]
Next, we can solve for \( x \). First, subtract 6 from both sides:
\[ 36 - 6 = 3x \] \[ 30 = 3x \]
Now, divide both sides by 3:
\[ x = \frac{30}{3} \] \[ x = 10 \]
Thus, Lucy has \( \boxed{10} \) seashells.