Two Japanese verbs can be coupled in one of the two ways:
1. i-stem verb + plain form verb
Examples: 逃げ回る、引き上げる、食べ歩く、読み終える、死に損なう
2. te-form verb + plain form verb
Examples: 逃げて回る、食べてみる、仕舞っておく、持っていく、飛んで行く
Both 逃げ回る and 逃げて回る mean to "run from place to place," or "flee here and there." Some people may see a subtle difference between the two, but I can't.
Similarly、食べ歩く and 食べて歩く mean (nearly?) the same thing.
You cannot say, however, 引いて上げる or 食べみる. There are no definitive rules about these matters. You must learn case by case for each word combination.
For details, google by using "te form compound verbs" , "テ型複合動詞" etc. as search words.