All insects have six legs. There are many many tiny ones. You need to be more specific.
Ants Earwigs have the pinchers or "cerci" at the back end.
You need to be much more precise. Insects have 6 legs. Spiders and other arachnids have 8 legs. Millipedes and centipedes have many more.
It sounds like the description of an assassin bug. Assassin bugs have a distinct orange head with pinchers for mouthparts, a striped body, and six legs. These bugs are beneficial predators that feed on other insects.
Pinchers in the back sounds like an earwig.
the lobster-like insect is called a 'pseudoscorpion'
I don't think there are bugs with four legs.
a bee
a stag beetle
If you encounter a large bug with pinchers in your backyard, it is best to avoid touching it and keep a safe distance. You can try to identify the bug from a distance and research if it is harmful or not. If you are unsure, it is recommended to contact a pest control professional for assistance.
a green and brownish bug that folds its front legs as if it is praying
A bug with six legs has six legs.