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The property of combinations states that if nCx = nCy, then either x = y or x + y = n.Case 1: x = yr - 6 = 3r + 1-7 = 2rr = -7/2.This value is not possible for r, as r must be a non-negative integer for combinations.Case 2: x + y = n(r - 6) + (3r + 1) = 434r - 5 = 434r = 48r = 12.We must also check that r-6 ≥ 0 and 3r+1 ≥ 0, and both are less than or equal to 43.If r = 12, then r-6 = 6 (≥0 and ≤43) and 3r+1 = 3(12)+1 = 37 (≥0 and ≤43). Both are valid.Thus, the value of r is 12.