Incorrect spelling, explanation: boundries is incorrect because of the missing letter a: the correct form is boundaries. Boundaries is a plural for boundary, which is a verb bound (to limit) with a noun suffix -ary. This suffix has a letter a which will also be visible in a plural form. We use this suffix for the loanwords from Medieval Latin, and bound is such a word.

Correct spelling, explanation: since boundaries is a plural form of boundary and the problem in question is whether is there a between d and r or not, let’s focus on the origins of boundary. It is a noun built from bound (verb) and a suffix -ary (noun suffix). Only by taking the suffix itself we can say why boundries is incorrect – there should be an a in the suffix. This suffix is used typically for Medieval Latin loanwords in English, and bound is taken from, indeed, Medieval Latin bodina. All of the above arguments point to boundaries as the correct form.

Definition of boundaries:
noun, limits, something that circumscribes where something ends
Without boundaries, it can be easy for others to take advantage of you or your time.
Knowing your personal boundaries can help you make decisions that align with your values and beliefs.

Phrases and collocations with boundaries:
set boundaries – show where are one’s limits
It’s crucial to set boundaries in any relationship, whether it’s personal or professional.
Cross boundaries To violate some established rules of behaviour
It’s never acceptable to cross professional boundaries by sharing confidential information.
Social boundaries – Limits that exist in particular social groups, usually based on ethical differences
In the past, there were strict social boundaries that divided different racial and ethnic groups in many societies.