**Explanation:**

The correct answer is option 'D' - brightly.

**The Sun is shining brightly** means that the Sun is emitting a strong and intense light. Here's a detailed explanation of why 'brightly' is the correct answer:

1. **Sunshine**: When the Sun shines, it means that its light is reaching the Earth and illuminating our surroundings. The Sun is the primary source of light and heat for our planet. It emits electromagnetic radiation, including visible light, which makes objects visible to our eyes.

2. **Brightness**: The word 'brightly' is used to describe the intensity of the Sun's light. When the Sun shines brightly, it means that the light is strong, clear, and vibrant. The brightness of the Sun can vary depending on factors such as weather conditions, time of day, and atmospheric conditions.

3. **Contrasting Options**: The other options provided in the question, such as 'cautiously', 'politely', and 'easily', do not accurately describe the quality of the Sun's light. These options are more suitable for describing human behavior or actions, rather than the characteristics of natural phenomena like the Sun's shine.

- 'Cautiously' implies a sense of carefulness or hesitation, which is not applicable to the Sun's shine.
- 'Politely' is used to describe courteous or respectful behavior, which does not align with the nature of the Sun's light.
- 'Easily' suggests a sense of simplicity or effortlessness, which is not specifically related to the intensity of the Sun's light.

In conclusion, the Sun shines brightly when its light is intense and vibrant, illuminating our surroundings. This option accurately describes the characteristic of the Sun's shine, making it the correct answer to the given question.