Albert Barnes Commentary Matthew 2:7

"Then Herod privily called the Wise-men, and learned of them exactly what time the star appeared." — Matthew 2:7 (ASV)

Privily. Secretly, privately. He did this to ascertain the time when Jesus was born.

Diligently. Accurately; exactly. He took pains to learn the precise time that the star appeared. He did this because he naturally concluded that the star appeared just at the time of his birth, and he wished to know precisely how old the child was.