Which one of the following two binomial factors of 6s2+40s-64

Factor 6s2+40s−646s2+40s−64=2(3s−4)(s+8)

To factor this we could use the ac method

we can first take out  2:-

f(s) = 2(3s^2 + 20s - 32)

3 * -32 = -96

so we look for factors of -96  that also add up to +20  and one must be negative
24  and -4   look good 
so we write

f(s )= 2(3s^2 + 24s - 4s - 32)

 =   2( 3s(s + 8) - 4(s + 8))

  = 2 (s + 8)(3s - 4)

theres your factors

Looks pretty good to me!