Given matrices A = [[3, 1], [6, 2]] and B = [[-1, 3], [3, 9]], calculate (A+B)A. Also, given 2M + 3AB = 2CB − BA, express M in terms of CB and AB.

Let $C = A+B$. We need to calculate $CA$.

The final answer is $\boxed{\begin{pmatrix} 30 & 10 \\ 93 & 31 \end{pmatrix}}$.

The given equation is $2\vec{M} + 3\vec{AB} = 2\vec{CB} - \vec{BA}$.
Subtract $3\vec{AB}$ from both sides:

Substitute $-\vec{AB}$ for $\vec{BA}$ in the equation:

Using the triangle rule for vector addition, $\vec{CA}$ can be expressed as the sum of vectors from C to B and B to A:

From Step 4, we have $\vec{M} = \vec{CB} - \vec{AB}$.
From Step 6, we have $\vec{CA} = \vec{CB} - \vec{AB}$.
Since both expressions are identical, we have proven that $\vec{M} = \vec{CA}$.
Therefore, $\boxed{\vec{M} = \vec{CA}}$.