Finding Coefficient in a Polynomial Function

Consider the polynomial function defined as:

$$P(x) = 2x^3 - 3x^2 + ax - 4$$

It is given that the function has a root at $x = 2$. This means that when $x = 2$, $P(2) = 0$. Additionally, suppose $P(x)$ can be expressed as a product of a linear term and a quadratic term: $$P(x) = (x - 2)(2x^2 + bx + c)$$

Using the information about the root, find the value of the coefficient $a$ in the polynomial equation. Express your answer as a decimal, and input only the numerical value without any additional symbols.