"For" is optional. The meaning does not change if you omit it. In general, periods of time do not require a preposition: "I slept eight hours", or "He's been studying English eight years". However, some expressions do require "for": "It feels like I've been waiting forever". You can't say "I've been waiting ever". "For one brief moment it I felt truly happy". "For the duration of the movie I felt hungry"

'For' in your sentence introduces the length of time of the action. It would be totally incorrect without it.

Good afternoon! In the phrase, "They were there for only two months when a neighbor's dog jumped over the fence," the word "for" is used to indicate the duration or period of time that "they" (referring to a group of individuals) were present or stayed at a particular location. If you remove the word "for" from the sentence, it would still be grammatically correct, but the meaning of the sentence would change slightly. The revised sentence would be: "They were there only two months when a neighbor's dog jumped over the fence." In this case, without the word "for," the sentence suggests that "they" were present or stayed at the location for exactly two months, emphasizing the specific duration. The original sentence with "for" implies that they were there for a period of two months but does not provide information about the exact length of time. Both versions are grammatically acceptable, but the choice to include or exclude "for" depends on the intended emphasis and the level of detail you want to convey.