Expanding (2-x)6 up to the term containing x2 gives :
64 - 192x +240x2
Multiply this by (1+kx) giving :
64 - 192x + 240x2 +64kx -192kx2 +240kx3
Since x2 should not be present the sum of the co-efficients of the x2 terms must add up to zero.
Therefore, 240 -192k = 0
k = 1.25