Why is the Entropy generation always positive?

Hint: First we have to know that entropy is a measure of molecular disorder or randomness of a given system and it can be created but it cannot be destroyed. Whereas the entropy generation is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes.

Complete answer:
Entropy of a system represented by the symbol \[S\]. If a reversible mechanism occurs in a system, then there is no net shift in entropy and entropy often increases in an irreversible process.
Thermodynamics’ second law states that the rate of generation of entropy within a system must be greater than or equal to zero. A process in which the rate of entropy generation is always zero is a reversible operation whereas irreversible processes lead to a high rate of entropy production.
Hence entropy generation is always positive within a system.

Additional Information:
 Entropy measures how much energy has been dispersed in a given process. We know that the flow of any energy is always from high to low. Hence, entropy always tends to increase.

Note:
Note that Entropy is generated when heat enters or exits a system. Heat is positive when entering a system and negative when exiting a system. The entropy changes of a system or its surroundings can be negative. Also note that there is a constant rise in the overall entropy of the universe.