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Let re-arrange this as follow:

A+B+C = 6 ——> Eq. 1

A*B = 2 ——–> Eq. 2

B*C = 6 ——–> Eq. 3

Case 1: Let say A=2 and B=1 => A*B = 2*1 = 2 This satisfies Eq. 2

Now, Putting above value in Eq. 1 => C= 3 —–> Eq. (4)

Put values of B and C in Eq. (3)

B*C = 1 * 3 = 3 != 6, This does not satisfies Eq. (3). Hence, A and B can not be 2 and 1.

Case 2: Let flip assumed values of A and B, thus new values of A=1 and B=2

Using these values Eq. (2) is satisfied i.e., A*B = 1*2 = 2

Again, using these values in Eq. (1) gives C = 3

Substitute, B = 2 and C = 3 in Eq. (3): B* C = 2*3 = 6

Since, assumed values of A = 1, B = 2 and C = 3 satisfies all above equations

C*A = 3 * 1 = 3

Therefore, C*A = 3 is the answer.