Explain why the planets do not twinkle.

Hint- The stars have their own energy sources whereas the light we receive from the planets is the reflected light of the stars that illuminates the planets and satellites. Also the earth is covered by a blanket of atmosphere that has different layers having different densities from the thinner to the thickest at ground level of the Earth.

Step-By-Step answer:
The light emanating from the distant stars, some of them are from millions of light years away, are in the forms of electro-magnetic waves and they vary in wavelengths from very short ultraviolet waves to very long radio waves. While theses gross spectrum penetrates into the atmospheric medium the light is refracted in varying degrees and therefore when we view from the Earth the visible light seems twinkling.

On the other hand the reflected light from the planets or satellites does not behave in this manner. Therefore the reflected light, mostly absorbed by the rough surface of the planets, and approximately 17–20 percent reflected light from the planets or satellites are experienced from the Earth. There is a slight deflection of the reflected light from the planets but very negligible for us to observe.
Additional information- The stars twinkle with the influence of our atmosphere in the night sky. As starlight hits our environment, currents in the atmosphere and regions with different temperatures and densities impact it. This makes the star light from the horizon to twinkle.

Note- The brightest planets (especially Venus and Jupiter) appear bright enough that the twinkling generally cannot dim them enough to be noticeable. Most stars, on the other hand, are only weakly visible to the unaided eye, so even relatively modest distortion is easily perceptible.