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The speaker doesn't seem to have a conflict. Not really internal or external at least. The fact is that he seems to have a task he needs to be doing, but he gets distracted. That could be a conflict. In the end he resolves this conflict by finding a cause that is greater than his current desire or obstacle. Which he does at the end, when he reminds himself that he has "promises to keep" and that's what allows him to keep moving through the woods.
On the other side of things he could be tired, or exhausted at the least. While it isn't normal for there to be something beautiful as a conflict, the woods in this case can be seen as just this. It can be seen as a temptation, or a lust in that sense, and him coming to his senses and realizing that he's chasing something more important. While acknowledging that it's hard, he at the same times knows this is an obstacle that he wants to overcome and that once he resist he will be able to rest. This is seen in the lines "The woods are lovely, dark, and deep. But I have promises to keep. And miles to go before I sleep, and miles to go before I sleep." There's actually a lot of conflicts and resolutions you can draw from this poem although it is short.
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