To determine the final position of point \( A(6, 8) \) after the described transformations, we will perform them step by step.
Step 1: Translation
The point \( A(6, 8) \) will undergo a translation of 2 units left and 5 units down.
- Translation 2 units left: \[ x: 6 - 2 = 4 \]
- Translation 5 units down: \[ y: 8 - 5 = 3 \]
So, after the translation, the new coordinates of point \( A \) are \( (4, 3) \).
Step 2: 180° Clockwise Rotation
Next, we will rotate the point \( (4, 3) \) 180° clockwise around the origin.
For a 180° rotation around the origin, the coordinates \( (x, y) \) transform to \( (-x, -y) \).
- Applying this transformation: \[ (4, 3) \rightarrow (-4, -3) \]
Final Result
After performing both transformations, the final coordinates of point \( A \) are \( (-4, -3) \).
Thus, the result is: \[ \boxed{(-4, -3)} \]