我喜欢一边吃东西,一边看报纸. jaco pointed out an interesting chinese grammar 一边。。一边 its doing things together at the same time. for example 我喜欢一边听音乐一边做练习。I like to listen to music while I do exercises. (as in study chinese exerceise etc)

Generally speaking, your sentence is right according to the grammar. Bcz, " 的时候"="when"(in a statement,not a question), so you can say anything as you like. This sentence is not the real Chinese way although there is no mistake, because you didn't give us your content or any hint, just a sentence only the grammar is a bit strange, so we have to use the whole sentence structure like"Subject + Verb + Object" is our Chinese way, as a result, all of the people who correct you add an object for the verb "吃", like "吃饭" "吃东西"etc. hope will help you more or less.

我喜欢一边吃东西,一边看报纸.

<我吃的時候,喜歡看報紙> 我吃東西的時候，喜歡看報紙。 吃東西: maybe eat an apple, or an icecream, or have lunch or supper. (eat anything that can be eaten)

我喜欢在吃饭的时候看报纸 如果你不打算在香港台湾生活或者去那里 你可以不学繁体字