Budh Homa or Mercury Homa is to appease the planet Mercury by performing Yagya or Homa and giving Ahutis for planet Mercury. It is very useful & beneficial puja, since it's worship strengthens benefic Mercury & increases its positive influence and pacifies malefic effects of the planet & neutralizes its negative effect. It is recommended for those having malefic Mercury or wrongly placed Mercury as per horoscope.
For eduction , marriage , if malefic Mercury in horoscop, performing brihaspati homa is highly recommended.
The planets are to propitiated against their evil influences, to ward off them, the Brihaspati Homa is done with faith to ward off all evils of Mercury as per the horoscope.
The Ahutis are given in the name of person who ordered Homa and Prashad is dispatched by courier to the devotee.