How to fix my flat tyre on my toyato 2013 model, the back wheel on the left passenger side a short nail from the board that grips carpet in place either was put there or i might have run over it,

Are you measuring this to to the tyre, the rim or the actual hub? Check the silly simple stuff first. Are they matching rims? Are they matching tyres? Are they BOTH at the same correct air pressure for where you are driving, (Hard for road, soft for serious off road)? Same 'size' rims can be a slightly different shape between manufacturers. Are you using 'spacers' between the hub and rim? If you are check they are in place, fitted correctly and the same thickness both sides. Tyres, especially the bigger 'off road' ones, can bulge if they are slightly under inflated or you are not parked on flat level ground when you measured it.
If all of these are all OK you will need to get the lift kit checked as something might not be fitted or lined up correctly.

There's not a lot to go on here but there are several things that cause this. Usually this will be caused by a wheel or tyre problem and to confirm this I would swap the two front wheels over and see if the wobble transfers to the other side. If it does jack up the side with the wobble and spin the wheel to see if the wheel and tyre run true, by this I mean the wheel and tyre don't show signs of buckling. If tyre is distorted but not the wheel buy a new tyre. If the wheel is distorted buy a replacement wheel and probably a new tyre. If neither tyre nor wheel are distorted and the tyre has plenty of tread left, take the wheel to a tyre distributor and have it rebalanced. If when you swapped the wheels around the wobble remained on the same side then there is probably something wrong with the steering or suspension components. With the wheel off the ground and the ca? secured on axle stands have an assistant pull the wheel around while you look for play in the joints and the wheel bearing. Worn components need replacement. Out of all the problems I have highlighted here, the wheel balancing is the most likely cause of your issues.

Check the suspension on that side. It could be a damaged spring or a blown shock absorber. Get the suspension linkages checked as well. There might be a loose or worn bush or mount.

Easy... Take cap off of liquid spray.... Hook up liquid spray end to where tire cap was and press button in liquid spray

Hi Elferns
Yep! You could do that
But the nail might damage the insides as you hit bumps.
Its a bit long winded but if you prop the car up on a jack and let the tyre down then break the seal from tyre to rim, you can reach inside with pliers and pull it out.
Also Better to use a marker on the outside to mark the entry point. You can buy a small kit with tools & rubber bead to push back in the original hole. The tool pulls out and leaves the rubber bead behind. Cut off excess.
Some people don't... but I prefer to coat the rubber bead with the included rubber glue before pushing into the puncture hole.
Kit available at 4WD shops.
Cheers

check if you tires have rayon cords or steel belts. this is a problem associated with the older tyres that had rayon cords as the main structure of the tyre. When left standing after running and allowed to cool the rayon belts actually took on a flat spot on the bottom and the noise lasted until the tyre warmed up enough for the tyre pressure to make the tyre round again. In extreme cold it may be the same for steel belted radials as the flat bottom of the tyre would hold the shape until the rubber warmed up .

take it back they have not set it up correctly. its alway best to do wheel alignment on new tyres, defects in worn tyres affect the alignment.

Rims can have tiny cracks too. A water test, where the wheel is completely submerged might show the source of the leak.

Your tyres need checking for slow punctures or leaking valves. If you want to do it yourself. You'll need a tub or pool big enough for a complete wheel. Fill it with water, then, remove one wheel at a time and put it in the tub/pool. look for bubbles, the puncture is where the bubble come from.

Of course you could go to a tyre shop and get them to check, once done and you know your tyres are in good order, the only other thought is that it may be someone having fun at your expense, you could get some lockable valve caps.

Simple. Need two people and also two vise grips, two smaill nails about 3 inches long. Put one nail in each vise grip and lock the vise grip onto the nail. Locate the plastic ring which can be found sitting on top of the seat and has a hole in it that one of the chrome braces fits in. Two chrome braces and two plastic rings. On the side of each of the rings is a hole. Take one vise grip and put the nail into the hole and you will feel it punch something in and when you release the push, the nail will return back out a very short distance. By pushing the nail in, you have released that brace. Now for the removal. You will need to punch into both plastic rings at the same time and then all you do is have the other party lift the head rest straight up and out. Piece of cake and there is absolutely no damage. To reinstall, simply place the two braces into the holes and push down and it will again be locked in. This was done on my 2007 Cadillac SRX.