Yes, that's a good direction. Now do the multiplication on the left to get two equations is a, b, c, d, and .

You should get and . We need to get rid of to have a condition on a, b, c, and d only so I would try dividing one equation by the other: so c-3d= -3a+ 9b. You can choose a value of any 3 of those and solve for the remaining one. You can find a basis by taking each of the 3 values equal to 1 in turn and the other two 0.