Entity-Relationship Diagram problem: trying to resolve a tentative many to many relationship
I'm not sure I entirely understand your question as it could be better structured, is this the structure you are looking for?

A CarType can have many cars BUT a car can only have one CarType. 1-to-many

A Mechanic can specialise in many CarTypes AND a CarType can have many Mechanics specialise in it. 
many-to-many

A mechanic can then work on multiple cars BUT a car can only be worked on by 1 mechanic. 
1-to-many

So when implementing the structure will look something like this: 

Hope this is of help, apologies if i haven't answered what you are looking for.