Determine c for 3 Real Roots in Polynomial

Consider the polynomial function defined by the equation:

$$ f(x) = 3x^4 - 16x^3 + 24x^2 - 8x + c $$

where $c$ is a constant. The function has exactly three real roots.

What is the value of $c$ that satisfies this condition? Enter your answer as a decimal or a fraction in the grid below.