The area of rhombus abcd is 120 square units.
ae = 12 and bd = x – 2. what is the value of x and the length of segment bd?

Area of the rhombus is:
A = ( d1 · d2 ) / 2
In this case:
d1 = AC and d2 = BD.
d1 = AC = 2 · AE = 2 · 12 = 24
d2 = BD = x - 2.
120 = ( 24 · ( x - 2 )) / 2
120 · 2 = 24 x - 48
240 = 24 x - 48
24 x = 240 + 48
24 x = 288
x = 288 : 24
x = 12
BD = 12 - 2 = 10

x = 12 units,  BD = 10 units.

What exactly is your question?