Appropriate time for second FUE hair transplant?

The appropriate time for a second FUE procedure would depend on your exam and consultation with your doctor.

It has been 6 months since your first FUE, you would like to have a second procedure to increase the density in the hairline. I would recommend waiting another 4-6 months or until you can see the growth of the first FUE. It is still too early. 

In FUE, the donor area could be harvested again now, if you where planning to have grafts implanted in another area of scalp. But, as you want more density in the area previously operated, you should wait until the final result: 10 to 12 months. It's too early to evaluate. Don't think only in number of grafts per cm2, a good result depends on a lot of other factors such as type of Hair, direction of implantation, thickness of the hair, number of hairs per graft and so on. In many cases, 33 grafts per cm2 will deliver a very good result. So, wait until your final outcome to have a decision.

At 8 months you can expect 80% of the growth from the hair transplant. At that time or shortly thereafter, you can have another hair transplant. Generally if you wait a full year, you will have 95% of the results from your first surgery so you will know what to do on the second surgery

It takes up to a year for the transplanted hair to grow in. If you want to transplant in the same area, I suggest  to wait until you get full hair growth in the recipient area before considering a second transplant unless you want to do different area then six months is alright. 

in order to thicken an area with a second hair transplantation,  I recommend waiting at least six months. I would also be using minoxidil in this period.