What is an example of Man vs. Himself with external conflict in Frankenstein by Mary Shelley?HAS to be external conflict!
This is an interesting and contradictory question, but it certainly applies to Frankenstein.
Essentially, your question is asking for an internal conflict that has external conflict. This novel's central character, Victor Frankenstein, deals with his own responsibility (internal conflict) to act on behalf of humanity (external conflict) for the entire book. For the majority of his actions, his internal conflict is his process through deciding to or not to act, while the external conflict is the consequence that his decision has for others.
One particular decision that contains this problem is his choice to create or not create a partner for the Creature. He feels remorse for having given the create life with no pleasure, but he recognizes that if he creates another monster, and a female at that, the two might reproduce monsters who could destroy humanity. No matter what decision he made, an external being would experience consequences. At that point, he would have to be in conflict with whichever being he displeased. For this situation, he chooses to displease the Creature and does not create a bride for the monster.
Now that you have this example, I am certain you will begin to see many others in Frankenstein.
Victor also experiences conflict with his "family" members - Elizabeth and Clerval, particularly - as they attempt to draw him him into nobler occupations such as his relationship with his family and the tranquil, salubrious contemplation of nature. Early in the novel, especially, he distances himself from these attempts. At the same time, he is struggling internally with his desire to create the creature, though he is aware that it is an abomination against nature and family.