Review the original item:
Sighing heavily, Melody tried to summon the energy to get to her next
class her heavy book bag and the long walk,
however, seemed impossible challenges.
You wanted to fix it this way:
Sighing heavily, Melody tried to summon the energy to get to her next
class but her heavy book bag and the long walk,
however, seemed impossible challenges.
Fixing this fused sentence with but alone is a problem. When you use a coordinating conjunction like but to connect two main clauses, you must also use a comma. In the example above, the comma is missing. In addition, there is already a contrast word, however. Two contrast words for one main clause is unnecessary repetition.
You might want to consult the rules for fixing comma splices and fused sentences.