The problem in the image is:

"Grafik fungsi $y = ax^3 - 2x^2 + 2ax + m - 3$ menyinggung sumbu $x$. Tentukan nilai $m$ yang memenuhi."

Translation: "The graph of the function $y = ax^3 - 2x^2 + 2ax + m - 3$ touches the $x$-axis. Determine the value of $m$ that satisfies this condition."

Solution:

If the graph of the function touches the $x$-axis, it means the function has a double root (i.e., the discriminant must be zero at that point). We need to analyze when the cubic function has a root with multiplicity 2.

1. Function: $y = ax^3 - 2x^2 + 2ax + m - 3$.
2. Condition: The graph touches the $x$-axis, so $y = 0$ has a repeated root.

Let's proceed with the necessary steps:

1. Find the derivative of $y$: $y' = \frac{d}{dx}(ax^3 - 2x^2 + 2ax + m - 3) = 3ax^2 - 4x + 2a$

2. **Condition for touching the $x$-axis: