Well, if your modem is currently connected to the coax close to the TV, then you will have a splitter there. Remove the splitter, modem & router and reconnect the TV there.
Then take the splitter to the white box in the garage. Disconnect the coax connection. The cable from outside goes into the splitter that has 1 input on a side. Connect the cable that was originally connected to the outside cable to one of the inputs on the 2 input side of the splitter. You should have 2 other coax cables (if a 2 bedroom). It will be a 50/50 chance of picking the correct one. Connect one. Then go to the room you want the modem in and connect the modem and router. If it all connects to the internet, you guessed correctly. If not go back to the garage and choose another coax. Keep trying until you connect the correct coax.
Want to make it easier and be able to label all of the coax in the garage? Do you have a multimeter? If not, you can get a useful one at Harbor Freight cheap - about $7. There is a harbor freight in Leesburg. 2257 Citrus Blvd, Leesburg, FL 34748
7 Function Digital Multimeter
and follow this video:
Trace coax wire
Just connect one of the short pieces of coax from your original modem/router installation to the wall jack in a room and have a point there to test with the meter. Should be able to test and label 2 or more coax in less than 15 minutes.