Answer:
The children wandered down the trail [with hiking sticks].
Did you read [about that car crash] [on the internet].
Shirley bought a new car [from the dealership][with better brakes].
Explanation:
Put the brackets around the preposition word and you close it when a noun shows up. Cross out the words in brackets and you have your new sentence. If your new sentence doesn't make sense, then it's wrong.