Given that ABCD is a rhombus with ADC = 120 degrees, and AD = 8 cm, OE = 2√2, and BD = 4 cm, we need to find the value of AE.

Since ABCD is a rhombus, all sides are equal in length. Therefore, BD = AD = 8 cm.

In triangle ABD, using the Law of Cosines, we have:
AB^2 = AD^2 + BD^2 - 2ADBDcos(ADB)
AB^2 = 8^2 + 4^2 - 284cos(120)
AB^2 = 64 + 16 - 64*(-0.5)
AB^2 = 64 + 16 + 32
AB^2 = 112
AB = √112
AB = 4√7

Since AE is the same length as AB, AE = 4√7 + OE
AE = 4√7 + 2√2
AE = 2√7 + 8

Therefore, the length of AE is 2√7 + 8 cm.