To transform \(y = f(x)\) to \(y = g(x)\), we perform the following transformations:

1. Stretch the graph of \(y = f(x)\) by a factor of 2 in the y-direction. This means that every y-coordinate of the graph is multiplied by 2.

2. Translate the resulting graph by \(\begin{pmatrix} -6 \\ 0 \end{pmatrix}\), which means shifting the graph 6 units to the left.

These transformations can be applied in either order to achieve the same result.