(A) "was at a complete loss for words" → Being so surprised by an unexpected job offer that one doesn't know what to say.
(B) "was dead on my feet" → Being extremely exhausted after a whole day of walking and sightseeing.
(C) "was at the end of my tether" → Being at the absolute limit of patience when dealing with children alone.
(D) "put a brave face to it" → Hiding upset feelings and pretending everything is fine in front of others.
Hence, Option 4: (A) - (III), (B) - (I), (C) - (II), (D) - (IV) → Each idiom perfectly matches the context: surprise and speechlessness for an unexpected offer, physical exhaustion after sightseeing, reaching the breaking point of patience with children, and masking emotions to appear composed → correct