To determine whether the given differential equation is exact, homogeneous, and linear, we need to understand the definitions and characteristics of these types of equations.

1. Exact Differential Equation:
An exact differential equation is of the form M(x,y)dx + N(x,y)dy = 0, where M and N are continuous functions defined on some open region in the xy-plane. It satisfies the condition ∂M/∂y = ∂N/∂x.

2. Homogeneous Differential Equation:
A homogeneous differential equation is of the form M(x,y)dx + N(x,y)dy = 0, where M and N are homogeneous functions of the same degree. A function f(x,y) is homogeneous of degree n if f(tx,ty) = t^n * f(x,y) for all t ≠ 0.

3. Linear Differential Equation:
A linear differential equation is of the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x.

Now, let's examine the given equation 2ydx - (3y - 2x)dy = 0.

1. Exactness:
To check for exactness, we need to compare the coefficients of dx and dy with the partial derivatives of M and N. Let's find the partial derivatives:
∂M/∂y = 0
∂N/∂x = 0

Since ∂M/∂y is not equal to ∂N/∂x, the given equation is not exact.

2. Homogeneity:
To check for homogeneity, we need to determine whether M and N are homogeneous functions of the same degree. Let's check the degree of each term:
Degree of 2ydx = 1
Degree of (3y - 2x)dy = 2

Since the degrees are different, the given equation is not homogeneous.

3. Linearity:
To check for linearity, we need to determine whether the equation is in the form dy/dx + P(x)y = Q(x). Let's rearrange the equation:
- (3y - 2x)dy = -2ydx
3ydy - 2xdy = -2ydx

The equation is not in the required form, so it is not linear.

Therefore, based on the characteristics of exact, homogeneous, and linear differential equations, the given equation 2ydx - (3y - 2x)dy = 0 is not exact, not homogeneous, and not linear. Hence, the correct answer is option 'A'.