1. The problem asks to describe the transformation from the function $f(x) = x^2 + 6$ to $g(x) = 4x^2 + 6$. 2. Recall that the general form of a vertical stretch or compression of a function $f(x)$ is given by $g(x) = a f(x)$ where $a$ is a constant. 3. Here, $g(x) = 4x^2 + 6$ can be rewritten as $g(x) = 4(x^2) + 6 = 4f(x) - 3 imes 6 + 6$ but more simply, since $f(x) = x^2 + 6$, $g(x)$ is $4x^2 + 6$ which is $4$ times the $x^2$ term plus the same constant $6$. 4. This means the parabola is vertically stretched by a factor of 4 compared to $f(x)$, but the vertical shift upwards by 6 units remains unchanged. 5. In plain language, the graph of $g$ is the graph of $f$ stretched vertically by a factor of 4, making it narrower, but it is still shifted up by 6 units. Final answer: The transformation from $f$ to $g$ is a vertical stretch by a factor of 4 about the horizontal line $y=6$.