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If  6  is one root, then  (x - 6)  is a factor.     So:  (x - 6)(x + ?)  =  x² - 2x + a

 

When you add  ?  to  -6  you must get  -2,  so  ?  =  4

 

The factors are (x - 6)(x + 4)  =  x² - 2x + 24

If 6 is a root , when you put in x= 6 the eq should = 0

6²-2(6) +a = 0

36-12+a = 0

a = - 24