A population of 1,200 leopards decreases by 12% per year. How many leopards will there be in the population after 6 years? Round your answer to the nearest whole number

After the first year, the population will decrease by 12%, leaving 1200 - 0.12*1200 = <<1200-0.12*1200=1056>>1056 leopards.

Similarly, after the second year, the population will be 1056 - 0.12*1056 = <<1056-0.12*1056=932.16>>932.16 leopards.
After 6 years, the population will be 932.16 - 0.12*932.16 = <<932.16-0.12*932.16=821.016>>821.016 leopards.
Rounding to the nearest whole number gives 821 leopards. Answer: \boxed{821}.