@jhul3z here is a subway map of the route from the cheongdam station to hongdae. You only have to make one transfer at Kongkuk University to get on the green line 2 (make sure you get on it going the right direction, I can post close ups so you can see the stops along the way or you should download the “jihachul” app if you have a smart phone). You are staying on the other side of the city so it will take about 45 minutes. Let me know if you have other questions about tmoney cards or where to go once you get out of exit 9.
hongdae
chungdam
seoul subway