This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. The on'yomi for 読 (どく) is the same as the reading in 読者. In case you forgot, think about how you just got a subscription to dock (どく) magazine. It's all about docks and dock related things. How exciting.