No. You don't have to pay for a full six months’ worth of car insurance coverage when there are only two months left on your six-month policy term.
When you place an additional vehicle on your car insurance policy while you are already in the middle of your policy term, you will be charged by your auto insurance provider only for the length of time still on your policy. Basically, your premiums for your new vehicle are pro-rated for the percentage of the policy still left.
In your scenario, you only have two months left of your six-month policy, so the price you pay is for the two months that the new car will be covered by your current policy.
When your car insurance policy renews, it will show all of the cars you own, including the new one, and the rates for all of your vehicles for the next six-month policy period.
If you know beforehand what vehicle you are going to purchase, then you can call your car insurance company and find out how much it will cost to add it to your existing policy. Your agent should also be able to estimate how much your car insurance rates will be for the next six-month policy with the new car added on.
When purchasing a vehicle, it is a good time to do a car insurance comparison and make sure you are getting the best car insurance rates for all of your vehicles. You may find that you already have the best rates available, or you may find that by changing companies you can save a few hundred dollars each year.
If you find better rates with a different car insurance company, then make sure to start your new policy before canceling out your old one so that there isn't a lapse in your car insurance coverage.