The correct answer is B. about to perish.
The phrase “on its last legs” means that something is about to die or fail. In this case, the business has been running for 12 years, but it is now in a state of decline. The partners may be trying to keep the business afloat, but it is likely that it will soon close down.
Option A, about to take off, is incorrect because the business is not about to succeed. Option C, about to produce results, is incorrect because the business is not about to achieve its goals. Option D, about to fructify, is incorrect because the business is not about to bear fruit.