Your box isn't perfect, so you won't be able to align your inner lines with both each other and their vanishing points, assuming you're drawing them in last. You need to eyeball the point where two inner lines will meet before you draw either line, the same way you do for the outer ones. They won't point perfectly towards their vanishing points, but you won't get a triangle.

Personally, the order I've been drawing my boxes in is: Front corner, two outer planes, the inner plane attached to them, final outer plane, final inner line. I've found this to make my inner lines much more accurate instead of leaving them all for the end.

First of all, your lines are very bold and confident. So congratulations on getting that part done. Coming to the box, try extending the lines of your box and you'll see that the convergence is very off. Take a little more time with your lines and try to aim for proper convergence. It's impractical to expect all the inner lines to converge perfectly, but if you ghost your lines properly and aim for a proper convergence, then you can reduce the gap for the inner lines convergence points.

I use the last convergence point to judge how well my box turned out. If it's close to perfection, then all my previous lines are also close to perfect. If the point of intersection is too far off, then one or more lines are may be going off the grid. When I do the error check, I can find out which lines are off the grid and try not to repeat the same mistake in my next set of boxes.

If you are finding this very difficult I recommend doing the rough perspective exercise once more. That exercise is all about aiming for convergence, so it might help you here as well.