To find the amount of parchment paper needed to cover the side of the cone-shaped funnel, we first need to calculate the lateral surface area of the cone. The formula for the lateral surface area \( A \) of a cone is given by:
\[ A = \pi r l \]
where \( r \) is the radius of the base of the cone, \( l \) is the slant height of the cone, and \( \pi \) is approximately 3.14.
Given that the diameter of the funnel is 6 inches, we can calculate the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
The slant height \( l \) is given as 4 inches. Now, we can substitute the values for \( r \) and \( l \) into the formula:
\[ A = \pi r l = 3.14 \times 3 \times 4 \]
Calculating the area:
\[ A = 3.14 \times 3 \times 4 = 3.14 \times 12 = 37.68 \text{ square inches} \]
Thus, the amount of parchment paper needed to cover the side of the funnel is
\[ \boxed{37.68} \text{ square inches.} \]