Generalizing $(^4C_0)^2-(^4C_1)^2+(^4C_2)^2-(^4C_3)^2+(^4C_4)^2=\,^4C_2$

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I got this question, and I have a bit of an issue with part (b). I managed to prove the attached result; however, it does not really fit the above result (as it said generalise the result and then prove). Can anyone assist?