In order to enable Mautic API log in to your Mautic Account and press the Setting icon in the top right corner.

Mautic Dashboard

 Then, choose  Configuration from the list of settings in the flyout menu.

Mautic settings

Finally, go to the API Settings tab and enable the API option. Besides, enable the HTTP basic auth options in case your API uses it (e.g. Magento 2 Mautic Integration extension)

Mautic API settings

Don't forget to press the Save&Close button.

Mautic settings save