Solution:

The equation of motion of the projectile is given as:

\[
y = 12x - \frac{3}{4}x^2
\]

At the range, \( y = 0 \). To find the range, set \( y = 0 \) and solve for \( x \):

\[
0 = 12x - \frac{3}{4}x^2
\]

Multiply the entire equation by 4 to eliminate the fraction:

\[
0 = 48x - 3x^2
\]

Factor the equation:

\[
0 = x(48 - 3x)
\]

This gives two solutions:

\[
x = 0 \quad \text{or} \quad 48 - 3x = 0
\]

Solving for \( x \):

\[
x = \frac{48}{3} = 16
\]