Question

how does carbon manage to exist in different forms? what are different forms?

Answer 1

carbon can exist in different forms because they have the tendency to react in different forms with different substances
Carbon exist in different forms like
coal,graphite, diamond, etc.

Answer 2

Carbon manage to exist in different forms bcoz of its catenation property I.e. self linking property with other atoms. And also due to its tetravalency which allows it to combine with different atoms like carbon,  hydrogen etc.