Thank you for the opportunity to help you with your question!

Since I don't know what your last two figures are, I'll have to guess. If I'm wrong, let me know. I'm guessing that the figure is a rectangle with the short side equal to 4 + 3(n-1) matchsticks in length and the longer side equal to 4 + 3(n-2) matchsticks in length. The area of the rectangle would be A = (4 + 3(n-1)) *(4 + 3(n-2)), If I want to fill the rectangle using exactly 599 matchsticks, then I must have A = 599. Solving for n, I have

or 9n^2 - 3n - 597 = 0. Using the quadratic formula with n in the of x, n ~ 8. You can then back substiture. Since n is not actually a whole number, I suspect my initial guess is incorrect. Clarify and I will correct.

Please let me know if you need any clarification. I'm always happy to answer your questions.