IMO C
1) not suff
a=-13, b=7
a=-20,b=14

2) not suff.
a and b can take any values as long as both are negative or both are positive

combined
the distance between them is 6

would go with C

stmnt 1. |a| – |b| = 6
let a and b be on either sides of 0 on the number line
let a=-10, b=4 distance between a and b is 14 (10+4)

let a and b be on the same side (both +ive or both ive)
say a=10, b=4 distance between a and b is 6 (10-6)
not sufficient


stment 2. ab > 0
=> either a and b both are positive or a and b both negative
=>a and b on the same side
no values are given, cant find distance.
not sufficient

combining, a and b on the same side
distance between a and b must be 6

hence, C