You see whatever you are looking for. Like most people, the female architects and engineers from the previous lessons also have to do laundry sometimes. Stop looking for things to complain about, and just enjoy the lesson. It's really well put together, and the content is fun and creative.
The women will put the laudry in the yard and the men will hang them up in the wind. It will give plesant shade and the odor will be nice as the men are studying in their home offices. When the kids come from school they will take the dried clothes down and carry them inside for grandma to iron them. When mom returns grandpa has already put them nicly together in the closets. Oh, what a wonderful world!
I think I can answer this one! It’s all about the vowels, and this is one of the ways that niqqud makes learning the language easier.
For most words, the definite article takes the vowel patach, and the following consonant is doubled with a dagesh: הַ◌ּ. So, for instance, נָשִׁים becomes הַנָּשִׁים. But the guttural consonants (א, ה, ח, ע, ר) cannot take a dagesh, and instead the vowel in the article sometimes changes before guttural consonants. The rules for this are complicated, and I’m relying on Wiktionary (https://en.wiktionary.org/wiki/ה־#Hebrew) as the best source I’ve found.
In this case, the word for yard, חצר, begins with ח followed by an unstressed qamats. And the rule says that the vowel in the article changes to segol. So חָצֵר becomes הֶחָצֵר. And when we attach the preposition ב־, it takes the same vowel as the article. So חָצֵר becomes הֶחָצֵר becomes בֶּחָצֵר.
This also means that, with very precise pronunciation, the vowel in בֶּחָצֵר (in the yard) should be a full “e” sound, rather than the reduced “e” from the sh’va in בְּחָצֵר (in a yard).