Generally, the bahuvrīhi is a compound whose members describe a third idea that is not explicitly stated:
(a woman) who has much rice
The bahuvrīhi is much less complicated than the tatpuruṣa, and we can account for most of its behavior with just a few rules:
शेषो बहुव्रीहिः। २.२.२३
śeṣo bahuvrīhiḥ (2.2.23)
The remaining samāsas are called bahuvrīhi.
Many related (padas) denoting a separate pada [optionally become a bahuvrīhi].
तेन सहेति तुल्ययोगे। २.२.२८
tena saheti tulyayoge (2.2.28)
tena saha iti tulya-yoge
The word saha [with a subanta] that has the same relation to the action (as the word it describes) [optionally becomes a bahuvrīhi].
महान् रथो यस्य → महारथः
mahān ratho yasya → mahārathaḥ
whose chariot is great (2.2.24)
(came) with his son (2.2.28)