Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2.?

Perimeter of quad. A
= 6 + 9 + 9 + 12
= 36

(Perimeter of quad. A) : (Perimeter of quad. B) = 6 : 2
36 : (Perimeter of quad. B) = 6 : 2

Perimeter of quad. B
= 36 × (2/6)
= 12

To compare the lengths of the shortest sides of A & B, get
Lb/La=2/6=1/3
=>
figure B is 1/3 of figure A in length
=>
the lengths of the other sides of B are:
9/3=3
9/3=3
12/3=4
=>
the perimeter of figure B=2+3+3+4=12.

Quadrilateral A, perimeter is 6 + 9 + 9 + 12 = 36 

Quadrilateral B is scaled by linear factor of 1/3

Hence, perimeter is scaled down by 1/3

i.e. perimeter of B is 12

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Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, 
with its shortest side of length 2.The perimeter of Quadrilateral B is 12.

Impossible to answer because polygon A is a three sided triangle and not a four sided quadrilateral.