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The 行けない is the negative potential form of the verb 行く. (「行く」= "go", 「行ける」= "can go", and 「行けない」= "can't go") The 歩いて here means "on foot", "by walking". 歩いて20分では行けない Think of it as the negative form of 「(ホテルまで)歩いて(20分で)行ける」, "can go (to the hotel) (in 20 minutes) on foot." 歩いて20分では行けないでしょう。 (Lit.) "You won't be able to go/get (there/to the ...
"v-て + time noun" means " time after verb" and "it takes time to verb" For example, 寝て一時間で起きた(I waked up a hour after sleeping), 走って一時間かかる(It takes an hour to run there). And "must not" is translated as してはいけない like 走ってはいけない(You must not run.) そこへは走っては行けない is translated as "You can't go there by running." and this 行けない is negative form of verb 行ける.
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