Yes, you can. "I barely can hear you" is good, but doesn't sound as good as "I can barely hear you". "I barely can't hear you" sounds bad but the reason has nothing to do with the placement of the adverb. It sounds confusing because it uses a double negative. "Barely" and "can't" are both negative ideas. Avoid double negatives.

Hi Yasozdal! Your sentence "I barely can't hear you" is not correct. The correct versions would be: "I can barely hear you." (meaning you can hear, but it's very difficult) "I can't hear you at all." (meaning you cannot hear at all) In general, you can place an adverb between the subject and "can." For example, "I can barely hear you" is correct because "barely" modifies the verb "hear." However, placing an adverb between the subject and "can't" usually doesn't work the same way. Instead, you should place the adverb after "can't" or rephrase the sentence for clarity. For instance, you could say, "I can't really hear you" to express a similar meaning.