Step 1: Identify the phrase meanings.
hard and fast: Rigid rules.
kith and kin: Family and friends.
hither thither: To and fro.
baited breath: (Incorrect spelling) Should be "bated breath" - anxious anticipation.
Step 2: Evaluate the sentence's meaning.The sentence suggests the Mayor filled positions through nepotism or favoritism.
Step 3: Choose the best-fitting phrase."Kith and kin" is the most appropriate, as it implies the Mayor hired people he knew personally (family and friends).