外贸中的法律文本或合同的语法与日常英语中使用的不同，这里的句子应当调整一下再理解：……代理协议~这句话指导下下。。谢谢~~
The Agent undertakes, in regard to each order or request of the Products, transmitted to the Principal from customers within the Territory to satisfy itself by means of proper inquiries as to the solvency of the customer.
the agent undertakes to satisfy itself by means of proper inquiries as to the solvency of the customer in regard to each order or request of the products transmitted to the principal from customers within the territory.
or
the agent undertakes to satisfy itself by proper inquiries about customer's solvency concerning each order or request of the products that are transmitted to the principal from customers within the territory.
这样一来，大意就比较容易理解了：
代理方自己确认客户方与每笔订单有关的资金/偿付力，订单相关的货物要转至境内客户委托方手中。
注：此处within the territory亦可能是指委托人的处所，或货物转移的位置，因其在句末，因此无法准确判断具体的修饰对象。
undertake
agree or promise to do sth 同意或答应做某事
in regard to
with respect to; concerning; with regard to
the principal
person for whom another acts as his agent, eg in business or law 被代理人, 委托人
territory
(extent of the) area for which sb has responsibility or over which a salesman, etc operates（某人负责的）地区（范围）; （推销员等的）营业地区
satisfy
FORMAL to provide someone with the evidence they need in order to be certain that something is true: CONVINCE
solvency
having enough money to pay one's debts; not in debt
2020年2月16日更新
代理方通过正常的查询（proper可理解为正常、按行业惯行的做法；inquiry有询价问价探听情况的意思）获知客户资信（solvency指资金偿付力，可理解为资金信用状况）以确保区域内客户方的任一订单或产品的洽购意向转至委托方。
另外，satisfy itself的itself从不同角度理解，也许可指agent自身，而不一定是each order or request of the products，那么可能理解为代理人完成自己的代理工作步骤。