The embedded clause is placed after the head noun "the man".
Typically, it is the head noun in the main clause that is reduced or missing.
Because the adjectives big and red modify this head noun, they are its dependents.
Some freedom, however, is allowed in the placement of adjectives relative to their head noun.
Modifiers to the head noun follow the order below.
All articles agree in gender, number and case with their head noun.
Possessive pronouns agree in case, number and gender with their head noun.
Within the noun phrase, the head noun is generally initial.
Numbers, however, can also follow the head noun.
Further, unlike an adjective, they cannot simply follow a head noun as an adjunct.