The phrase "great grandson" refers to the child of your grandson or granddaughter. It means that they are your great-great-grandparent's great-great-grandchild. Full definition
Now, for my problem, I have a 9 year old great grandson. (happyhooligans.ca)
Chris Darwin is a great great grandson of Charles Darwin. (meatfreemondays.com)
John Call... Great great grandson of Winfield Scott survivor Asa Cyrus Call, shares Asa's experiences as a passenger and survivor aboard the side - wheel steamer Winfield Scott durning the California Gold Rush. (channelislands.noaa.gov)