How do I solve these type of questions and get the answers as below?

Find a constant portfolio consisting of European calls and/or puts that replicates the European derivative with maturity T and pay-off Y.

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Y 4 3 2 1 S(T) 2 4 6 8 10 Remark: For S(T) > 10 the pay-off is identically zero. Solution: (-2P(1), 2P(3),3/2C(4), -3C(6),3/2C(8)), where C(K), P(K) are the call and put with strike K and maturity T. Remark: other solutions are possible. 2 Y 1 1 2 2 3 4 5 S(T) -1 -2 -3 Remark: For S(T) > 4 the pay-off is identically zero. Solution: -1 share of the put with strike 1, -3 shares of the put with strike 2, 1 share of the put with strike 4. Y 4 3 2 1 S(T) 2 4 6 8 10 Remark: For S(T) > 10 the pay-off is identically zero. Solution: (-2P(1), 2P(3),3/2C(4), -3C(6),3/2C(8)), where C(K), P(K) are the call and put with strike K and maturity T. Remark: other solutions are possible. 2 Y 1 1 2 2 3 4 5 S(T) -1 -2 -3 Remark: For S(T) > 4 the pay-off is identically zero. Solution: -1 share of the put with strike 1, -3 shares of the put with strike 2, 1 share of the put with strike 4