How can I find the Vehicles compatible with a Motors Part Item using eBay API?

You can use the api call : getProductCompatibilities (http://developer.ebay.com/DevZone/product/CallRef/getProductCompatibilities.html)

You can call this API in 2 ways, POST request(using SoapUI) or just test the request in your browser(GET).

GET:
You can do a simple GET request : http://svcs.ebay.com/services/marketplacecatalog/ProductService/v1?OPERATION-NAME=getProductCompatibilities&SECURITY-APPNAME=YourAppId&productIdentifier.ePID=74488836

(put in your app id)

POST request:

WSDL : http://svcs.ebay.com/services/marketplacecatalog/ProductService/v1

<?xml version="1.0" encoding="UTF-8"?>
<getProductCompatibilitiesRequest
xmlns="http://www.ebay.com/marketplace/marketplacecatalog/v1/services">
<productIdentifier>
<ePID>74488836</ePID>
</productIdentifier>
<!--
<applicationPropertyFilter>
<propertyName>Make</propertyName>
<value>
<text>
<value>Mercedes-Benz</value>
</text>
</value>
</applicationPropertyFilter>
-->
</getProductCompatibilitiesRequest>

Headers : X-EBAY-SOA-OPERATION-NAME ,X-EBAY-SOA-SECURITY-APPNAME, X-EBAY-SOA-GLOBAL-ID

This will retrieve all the vehicles in the list however you can apply an application property filter. like shown below.

<applicationPropertyFilter>
<propertyName>Make</propertyName>
<value>
<text>
<value>Mercedes-Benz</value>
</text>
</value>
</applicationPropertyFilter>

Also attached a screen shot of the SoapUI request.