In Greek, a compound verb is a verb that consists of a merger between a preposition and a verb; e.g. εκβαλλω is a compound of the preposition εκ and the verb βαλλω.
Compound verbs form their tense stems the same way as the simple verb. For example, the future of βαλλω is βαλω. Likewise, the future of εκβαλλω is εκβαλω.
When adding an augment to a compound verb, you will place the augment after the preposition and before the stem of the verb. Hence, the imperfect of καταβαινω is κατεβαινον.
Note: if the preposition ends with a vowel as κατα, that vowel will elide as it did in κατεβαινον.
Reduplication also occurs to the verb stem, not the preposition; e.g. εκβαλλω (present) εκβεβληκα (perfect).
Don’t confuse a compound verb with a compound predicate.