A LED device has these specifications:
Red (wavelength 633 nm). Power output 8.4 mW/cm2. A mW is a milliWatt, or a thousandth of a Watt.
The light output is 8.4 mW per cm2 and your goal is 4 Joules per cm2 per treatment. One Joule is defined as one Watt per second, so in order to achieve that, you should know that J = W x S (Joule is Watt x Seconds)
In our case, we want to know how many seconds, so our equation becomes S = J / W. We just said 4 Joules is the target energy to be delivered to a square centimeter of skin, and the output of LED devices is stated in mW, so the formula to use is: Seconds of treatment per cm2 of skin = 4000 mJ / milliWatt per cm2 of skin.
4000 mJ divided by 8.4 = 476 seconds.
So each time you use the device, you should apply it for 476 seconds (8 minutes) on a skin surface area with the same size as the light emitting surface area as the device. This means that if you want to treat a skin area that is four times larger than the light emitting part of the LED device, that you need to move it over the skin for 4 x 8 = 32 minutes in total.
If the output per cm2 is not specified, look for the total output of the device and divide the total output by the total area of the panels with LEDs. This will give the Wattage per cm2. Example: Output area is 10 cm2, total Wattage is 50 mW. Wattage per cm2 is 50 divided by 10 = 5 mW.