Idiom: Permit ... to

Idiom

permit someone to do something

Option A.
this option begins with the use 'which'
'which' is a determiner that is use majorly for interrogative sentence or questions.
Therefore, it is improper to introduce the preceding clause with 'which'
alternatively 'which' can be use relatively giving expression to a sentence.

Option B.
This option is also guilty of the error in Option A.It suffers the same fate as the previous option.But it also contain more conflicting grammatical errors 'employees balancing home and work responsibilities better will realize' this is grammatically incorrect ,because of the introduction of 'balancing'

Option C.
'that' is acting as a conjunction here for introducing a clause which is the subject or object of a verb(such as one involving reported speech),or which is a complement of the previous statement.
Also,the conjunction 'that' is used to introduce a subordinate clause expressing a reason or a cause.This clause expresses and aim,such as in the sentence above and it usually contains auxiliary verbs.
Option C duly satisfies the explanation above and THEREFORE THE CORRECT ANSWER IS OPTION C.

Option D.
beween?????
It is absurd! In plain interpretation of the whole question talks about 'balance'
The use of 'balance between' looks awkward and does not follow proper parallelism.
Also,this is grammatically wrong!

Option E.
THis option is incorrect,the use of 'such' as an introductory determiner is basically use for comparison with something implied by context.
The question in any way does not show comparison and this makes the option incorrect.