So, in light of the above, you can say that this could be an example of mansplaining, particularly if your wife already knows what an alternator does, and already understands the concept of doing the work yourself as opposed to paying somebody else to do it.You need to explain what it is that exactly turns you off to the conversation. As an example, if I explain to my wife the function of the alternator in our car, how to replace it, and why doing the work myself is less expensive than going to a mechanic, would that be mansplaining?
If your aim in the conversation is to demonstrate your superior knowledge of alternators to your wife, assuming that women generally don't know much about cars, then you might be mansplaining.