Abcd is a rectangle. the length of bd is 8 units, and m angle abd is 67°. the length of ac is units, and m angle cdb is °.

See the attached picture to better understand the problem
we know that
in rectangle ABCD 
AB=CD
and 
AD=BC
therefore
the triangle ACD and triangle ABC are congruent
so
BD=AC
BD=8 units

the answer part a) is
BD= 8 units

Part b) Find angle CBD

we know that
∠ABD+∠CBD=90°---------> by complementary angles
so
∠CBD=90-∠ABD-----> 90-67----> 23°
∠CBD=23°

the answer Part b) is
∠CBD=23 degrees