The question asks which transformations carry the given regular polygon (a hexagon) onto itself. Let us analyze the options:

1. Rotation of 300° clockwise:
   A hexagon is symmetric and can be rotated by multiples of $360°/6 = 60°$ to map onto itself. A 300° clockwise rotation is equivalent to $360° - 300° = 60°$ counterclockwise, which maps the hexagon onto itself.
   ✅ Correct.

2. Reflection across $\ell$:
   Regular polygons are symmetric along their axes of symmetry. The line $\ell$ shown in the image appears to be one such axis of symmetry for this hexagon. Reflecting across $\ell$ maps the hexagon onto itself.
   ✅ Correct.

3. Rotation of 300° counterclockwise:
   A 300° counterclockwise rotation is equivalent to $360° - 300° = 60°$ clockwise. As previously established, rotations by multiples of 60° map the hexagon onto itself.
   ✅ Correct.

4. Rotation of 120° clockwise:
   Rotating the hexagon by 120° clockwise (which is $2 \times 60°$) is another valid transformation because it corresponds to one-third of a full rotation, which maps the hexagon onto itself.
   ✅ Correct.

Thus, all the listed transformations carry the hexagon onto itself.

Would you like more detailed explanations?

Related Questions:

1. What are the general rules for symmetries of regular polygons?
2. How can you determine the number of lines of symmetry for a regular polygon?
3. Why does a 300° clockwise rotation match a 60° counterclockwise rotation?
4. Can any irregular polygon have the same rotational symmetry as a regular hexagon?
5. How is reflection symmetry connected to rotational symmetry in polygons?

Tip:

For regular polygons with $n$ sides, rotations by $360°/n$ and reflections across axes of symmetry are always valid transformations that map the shape onto itself.