let

c = quarts that Charlie picked

n = quarts that Noel picked

Charlie and Noel picked 92 quarts at the king's orchard

c + n = 92

Charlie picked 6 more quarts than Noel

c = 6 + n

plug c = 6 + n into c + n = 92

6 + n + n = 92

by solving the equation we find

n = 43 quarts

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Noel picked 43 quarts.