Shipping Costs Based on Distance
Magento Shipping Debug

As the Shipping Costs Based on Distance extension requires a valid Google route/distance matrix API key from it can happen that this API isn't activated or valid, in that case the method doesn't show up on the front-end.

To get an insight on why it's not showing you can enable the Logfunction which is available in the extension since version 1.8.5

You can enable the debugging option to write all the Google API calls to the logfile var/log/shippingperkm.log.

After enabling the log function you can check the shipping method throught the front-end and check the logfile again. This can be an output like;

2018-10-11T07:42:42+00:00 DEBUG (7): Shipping Distance Error: {"destination_addresses":[],"error_message":"This API project is not authorized to use this API.","origin_addresses":[],"rows":[],"status":"REQUEST_DENIED”}

Which tells that the API Key isn't authorized on the specific domain.