Lets take the biggest number possible with 8 bits i.e., 1111 1111
Now since the question asked for 2's complement then MSB is reserved for sign bit therefore considering sign bit, biggest number possible with 8 bits is:
(+/-bit) 111 1111
Smallest number possible will be the reverse of this number:
(+/-bit) 000 0000
Now as per convention 1 is for -ve and 0 is for +ve therefore smallest number will be:
1 000 0000
Which comes out to be -128.