I think you are understanding it a bit wrong. What I understand from the picture is that if we have a optically active molecule and we have to find its meso stereoisomer then we rotate groups of a chiral atom untill internal plane of symmetry is achieved. This is right but will work in a very few cases.
You are right that rotating groups will change its optical activity that is why it became optically inactive from being optically active initially.
There is no such exact way of judging whether molecule has plane of symmetry or not but there are some points you should note:
1. Planar molecule always has a plane of symmetry through the plane of the molecule hence always optically inactive.
2. If there are odd nos of chiral atoms then there will never be a plane of symmetry.(not considering pseudo chiral)
3. Always try cutting the molecules through atoms in a line which are different, collinear to the centre of molecule and check if that is a plane of symmetry or not.
4. You should also check centre of symmetry if it exists in the molecule.
In meso compounds there is internal racemisation which means that overall plane polarised light does not rotate when interacts with molecule. This is because one half of the molecule acts as dextro rotatory and other acts as laevo rotatory as the molecule has plane of symmetry. Hence one part rotates the light but other part rotates it in other direction with equal magnitude due to symmetry. Hence meso compounds are optically inactive.