the picture in the attached figure
we know that
ZY=4 cm
AB=XY------> 2 cm
ZX=ZY-XY------> 4-2----> 2 cm
in the right triangle AXZ
applying the Pythagorean Theorem
AZ²=AX²+XZ²-------> solve for AX
AX²=AZ²-XZ²------> 8²-2²-----> AX²=60------> AX=√60-----> AX=2√15 cm
BY=AX
BY=2√15 cm-------> the length of the common tangent
the answer is
the length of the common tangent is 2√15 cm
