Divorcing this from a specific context makes all the answer academic, contrived, and almost entirely useless.
In what corporate monstrosity is this type of communication happening?
There is no real way to determine what to do. Communication is the only antidote to the political nonsense Jane and her boss are potentially trapped in, but this is too sanitized to even know. Without that background, this and any specific advice is just as likely to be wrong as right. I could spin stories in any direction that would make an answer obvious in one context inappropriate in another. In most companies, Jane and her boss^1 are weighing the political capital they need to spend to resolve this, which is entirely unrelated to actually completing the project, which I guess we're supposed to assume is important?
What's the project? Is the deadline important? Did Jane's boss^2 ask her because there's some critical business need that prevented her from waiting for boss^1? Did Jane's estimate already reach a customer's ears? Can Jane reduce the actual time by pulling on other resources, perhaps meeting or exceeding the estimate? Is Jane's boss performing? Does the culture encourage people to not work hard, to prevent others from looking bad?
Look at this question: "Which of the following decisions should Jane take to avoid offending her reporting officer and the director and why should Jane take that decision?" Offending them? Offending? Is this work or school? There are people who have the social skills to have a simple conversation with boss^1 and boss^2 and have everyone leaving happy. There are others who offend everyone, even under complete agreement. How long does the work actually take, what quality is required, what debt (technical debt, administrative debt) would be left behind--these all need to be answered. Let's say Jane is a programmer. Maybe Jane explains to boss^2 that she hadn't considered technical debt, and that she can deliver functional code in 5 days into production, but that she'll need to account for an additional 5 days to resolve the technical debt. If that's the reality, whether boss^1 or boss^2 is offended is impossible to predict. Boss^1 may be offended unless Jane intentionally offends boss^2, due to some territorially nonsense that doesn't belong at work and will probably exist in whatever monstrosity of a corporate structure is assumed in this case.
Questions like this are loaded--they encourage generic "why can't we all just get along" answers rather than constructive solutions from the details, and totally ignore the hundreds of other factors that could change everyone's answers. I could repost this with different details filled in and get the exact same members posting contradictory advice, and they would often be correct. If this is for some type of training material, frankly, it's a disaster on multiple levels. If it's been sanitized from a real-world situation, please include enough details to make it meaningful.
So here's my answer: (d) Jane should put down the textbook and look for a job in the 21st century.