I'm going to respectfully disagree with Mike's answer. Starting workflows with a 1 minute pause is good practice, but the symptoms are different than what you're experiencing here: if your workflow randomly throws errors about not being able to update an item because it requires a different content type, you need to add that 1 minute pause.
In this case, where the "if" condition is never resolving as true but the workflow is progressing without an error otherwise, the most likely culprit would be at Current Task:Assigned To. One huge annoyance about workflows, sharepoint designer, and sharepoint in general is that it'll often display things differently than they're seen on the backend. Perhaps it's using usernames or display names, where "Car" is in one but not the other. Try setting a workflow variable to Current Task:Assigned To, then logging the value, then testing the variable against "Car". That'll at least progress your troubleshooting. Alternatively, do it before entering the approval workflow: set the value in Current Item to whatever you're using to pick "Assigned To" for the approval workflow.