申请居家办公Requesting Permission to Work from Home

for the next six months starting from the beginning of the next month

明确申请的时长和起始范围，符合核心请求。

it would definitely help me save a lot of time that is wasted commuting to and from the office

通勤时间是直接相关的申请理由，随后距离和压力进一步解释个人需求。

This arrangement would benefit both me and the office as I would be able to work more hours per week to finish the deadlines.

明确回应双方收益，但公司受益的说明只有笼统增加时间，展开有限。

And I am dubbing this a “great opportunity” because

读者能理解指的是居家办公，但段首And及临时命名式表达使承接显得突兀。

Moreover, less time in road traffic could also mean less stress, and when we have more time to finish our work and less stress, we are usually more productive at work.

有从通勤到压力再到效率的因果链，但time与stress在同一句中反复出现。

I am hoping that you would agree to let me work from home for the next six months starting from 1st February.

结尾回到申请目的，但与首段几乎重复，新增信息主要是具体日期。

seek your permission to avail the “work from home” facility

能理解申请意图，但avail通常需用avail myself of等结构；将政策称为facility也偏生硬。

wasted commuting to and from the office

commuting准确描述往返办公室的通勤活动，主题词汇有效。

to finish the deadlines

deadlines不能与finish如此搭配，应表达赶上期限或按期完成工作。

especially, when I live a bit too far from my office due to some family reasons.

when从句可以理解，但especially后不宜用逗号割开修饰关系。

when we have more time to finish our work and less stress, we are usually more productive at work.

时间条件关系清楚，从句与主句安排准确。

This arrangement would benefit both me and the office as I would be able to work more hours per week

情态动词和as原因从句使用基本准确。