Destroy and destruct are synonyms to each other.

Synonyms are the pair of words which have similar meanings to each other and may be used in each other’s place.

Destroy as verb:

In English language, destroy is used as a verb which means to end something or its existence.

Example:

All houses were destroyed by the flood.

Destruct as verb:

Destruct is also used as a verb in English language which means to destroy something deliberately.

Example:

The war destructed the entire infrastructure.

Both these words are synonyms and can be used interchangeably. Although destroy is somewhat a mild form of ending existence whereas destruct is more grave destroying of something.