They gave out （说）that （宾语从句）。下面括号里全部是宾语从句。这里的宾语是gave的宾语。
They gave out that （they knew how to weave stuffs of the most beautiful colors and elaborate patterns , the clothes manufactured from which should have the wonderful, property of remaining invisible to everyone who was unfit for the office he held, or who was extraordinarily simple in character）.
下面分析宾语从句。
they knew （宾语）。下面括号里全部是宾语。这里的宾语是knew的宾语。how to do something 结构做宾语（我不清楚这算不算不定式结构，忘了中学英语中是如何进行语法分类的）
they knew （how to weave stuffs of the most beautiful colors and elaborate patterns , the clothes manufactured from which should have the wonderful, property of remaining invisible to everyone who was unfit for the office he held, or who was extraordinarily simple in character）.
下面分析宾语。
how to weave （宾语）。括号里面都是weave的宾语
how to weave （stuffs of the most beautiful colors and elaborate patterns , the clothes manufactured from which should have the wonderful, property of remaining invisible to everyone who was unfit for the office he held, or who was extraordinarily simple in character）.
下面分析宾语。
stuffs （of 后置定语），（which引导的非限定性定语从句）
宾语：stuffs of the most beautiful colors and elaborate patterns，最漂亮的颜色和精致的花纹的东西。of表示后面修饰前面。比如the door of the room，那个房间的门。
which引导的非限定性定语从句：clothes manufactured from which should have the wonderful, property of remaining invisible to everyone who was unfit for the office he held, or who was extraordinarily simple in character
通常定语从句的引导词放在句首，如I like the table which is pink. 但如果引导词在定语从句中做介词宾语，如I like the table which the cat is sitting on，很多时候会把介词放到引导词前面，如I like the table on which the cat is sitting.
这里的这个定语从句就是这样的。它的结构有点复杂，我写个类似结构但简单的：I like the table the cat sitting on which is red. 意思是我喜欢那个桌子，什么样的桌子呢，那个猫坐着的那个桌子，那个猫是红色的。如果要直译，就是我喜欢那个桌子，那个坐在那个桌子上的猫是红色的。在中文里，肯定该不会用这种复杂的句子来表达，会拆成两个句子。但在英文中，这种定语从句的表达会比较方便，不用这个那个不停的用，但同时造成了结构很复杂，理解起来很困难。
这个which引导的定语从句的结构是：
the clothes manufactured from which should have the wonderful, property （定语）
（括号里面都是定语。另外要注意一下，wonderful和property两个词之间的逗号，是不应该有的，我想可能是提问者笔误）
the clothes manufactured from which should have the wonderful, property （of remaining invisible to everyone who was unfit for the office he held, or who was extraordinarily simple in character）
这个定语的结构是 of remaining invisible to everyone （who定语从句,or who定语从句）
who was unfit for the office he held, or who was extraordinarily simple in character.
综上，整个句子结构是：
They gave out that （1宾语从句 they knew （2宾语 how to weave （3宾语 stuffs of the most beautiful colors and elaborate patterns 3）, （4 定语从句the clothes manufactured from which should have the wonderful, property （5 定语 of remaining invisible to everyone （6定语从句who was unfit for the office （7that引导的定语从句，that省略了 he held 7）6）, or （8定语从句who was extraordinarily simple in character. 8） 5） 4）2）1）
直译：
他们指出一些东西（宾语从句1）。
他们指出的是， 他们知道一些东西（宾语2）。
他们知道的东西是如何编织一些漂亮颜色和精致图案的东西（宾语3）。
（定语从句4）用这些东西做的布有一些很神奇的特性（多么神奇呢，见定语5）。
（定语5）这些布对每个人都是不可见的（哪样一些人呢，见定语从句6和定语从句8）。
（定语从句6）这些人不适合那些职位（哪些职位，定语从句7说了，他正在干的职位）。
（定语从句8）这些人头脑特别简单（也就是特别傻的意思）。
组合成中文，就是：
他们说，他们知道如何编织一些漂亮颜色和精致图案的东西，用这些东西做的布有一些很神奇的特性，这些布对那些不适合他们现有职位的人或者特别愚蠢的人是不可见的。
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