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I understand there are some properties in an organic compound that allow stereoisomerism.

  • double bond can't rotate

  • two double bonded carbon atoms each have two different atoms or groups attached

I'm unsure by the meaning of two different atoms/groups around on each side of the double bond.

enter image description here

With respect to but-2-ene. From my understanding, both sides of the carbon atom have $\ce{-CH3}$ on either side of the double bond so how does this comply with the rule that "Two different atoms or groups attached around each carbon of the double bond"

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Stereoisomers are different due to the spatial arrangement of their atoms.

The picture that you gave has two $\ce{CH3}$ groups on one side. That is called cis - as they are on the same side. There is another isomer, called trans. That is when one of the $\ce{CH3}$ is on the top and the other $\ce{CH3}$ is at the bottom. The arrangements of the $\ce{CH3}$ and $\ce{H}$ is different in cis and trans.

This link explains it well: Chem.Libretexts

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