What is the difference between 同意 and 合意 ?Feel free to just provide example sentences.

合意 is a “mutual” agreement. Party A and Party B are a counterparty to each other, and both A and B reach an agreement on the same matter.
同意 is not a mutual but a one-way agreement. Party A proposes/argues something first, and then Party B agrees with it (or approve/vouch for it, or support/advocate it).

Here are examples:

イギリスとEUはBrexitに関して合意に達した。
UK and EU reached a mutual agreement on Brexit.

Brexitの交渉期限のさらなる延長をイギリスが要請し、EUがこれに同意した。
Re: Brexit, UK requested further extension of the negotiation deadline, and EU agreed with (or accepted) the inquiry.

同意 is also frequently used in waiver forms. For instance, a doctor asks his patient to sign a waiver form of a clinical trial of a new drug. After signing the 同意書, the patient (clinical trial participant) cannot sue for any side effects. 同意書 is translated as “consent agreement”, which is one-way, not a mutual one.