"Best way" ? Only legal way is to get an EPA licensed Heating and A/C contractor (your Search the list category to find well-rated and reviewed companies for this) to fix the leaks and then repair and refill the system.
The 2 of 6 gallons is more likely 2 of 6 pounds, right ? - about 6 pounds would be in the normal range for a 2 ton unit. Freon weighs about 10-11 #/gal depending on temperature/pressure, so a 6 gallon capacity would be around 60-70 # of Freon - WAYYY beyond anything one would expect to see in a residence - that would be a commercial building size air conditioning system capacity of probably around 15-30 ton cooling capacity.
As for cheapest - some HVAC contractors roll the charging labor into the gas cost, some charge separately for labor, so cost can vary a lot jusat due to that reason. Generally, R-22 (Freon) currently costs about $25/lb give or take (in contractor size canisters) - around $50/lb plus or minus is a common charge for it without labor, although some are charging as much as into the $100-200 range - some with labor, some without. Labor for a refill of 6# (on top of the leak diagnosis and repair cost) is likely to be about $50-100 if done at same time as the repair - probably more like $100-200 just for a top-off (though that is generally illegal if the leak(s) are not repaired.
You could call around to see who has low R-22 prices, but the repair is likely to be the major part of the job - certainly ask what the fee is from contractors you talk to to be sure you don't get one gouging on the price, but another hundred or two difference is not likely to make or break the job cost.
R-22 is going out of production, but should be around for another 3 years or so as new production/imports - and recycled R-22 will be available for a short time after that. However, there are several replacement legal gases which can be substituted for R-22, though may require a system flushing before use because the lubricants are sometimes incompatible, though there is at least one which is a "drop-in" gas suitable for many brands of units. Currently, those gases run 50-100% of the cost of R-22. So - if keeping your unit running is economic I would repair and refill it - if the repair cost is high (including the gas repalcement) you might consider replacing the entire unit.
Of course, WHERE the leak is is very important too - a lineset leak at a connection can be readily fixed - a corroded leaking evaporator coil (a very common place for leaks in older units) can run into the $1500 plus or minus $500 range commonly - in which case you are into roughly half the cost of a new unit and might best be considering replacing the 11 year old unit.
Also - depending on the situation, like if the lubricant in the refrigerant is scorched due to compressor overheating because of the low refrigerant level, the lineset may need to be flushed and the remaining gas removed and disposed of instead of reusing it as would normally be the case if the unit was "clean" inside and just low on gas. Opening up the filter/drier and checking for scorching and/or sludge or metal parts (indicating compressor failure) is needed to assess that - and after a signfiicantly low refrigerant event the filter/drier (or its cartridge if a cartridge type) should always be changed out anyway.
You can find a number of previous questions with answers about the repair/replace decision and the economics involved, and how your expected residency in the house affects the economics of higher efficiency versus minimum efficiency unit selection - look in the home > HVAC link under Browse Projects, at lower left.
