In every example except in the one in the image below the hint “requested” is translated as ように頼む how do I know that in this specific example I have to write ように言う?
Also the hint “told” only once is translated as ように頼む.
This is the example I am talking about
掃除そうじ終おわったばかりなのに洗あらい物ものもするように頼たのまれた。
Even though I had just finished cleaning the house, I was told to do the dishes. [in such a way]
I agree with you that it seems somewhat inconsistent, but here’s my best guess after reading through all the sentences.
It seems like all the 頼む sentences have a hint of “entrusting” to them (another definition of the word), which arguably doesn’t exist in the sentence you’re asking about (the one in the picture). Again, this is just a guess, but I figured I’d still mention it.
@seanblue @Seanm826
I am awfully sorry for such confusing sentences!
I changed the “ように言う” sentence to “told” and “ように頼まれた” to"requested" respectively.
The ように[頼む/言う/命じる(rarer)] is used to indirectly bring someone’s utterance. (Reported speech)
The difference is, when a person uses 頼む the original message was a request rather than order, so the speaker was originally told: 皿を洗って(ください)。
If the speaker said the same thing with ように言う then it could have been originally both order 皿を洗いなさい/皿を洗え or request 皿を洗って(ください).
And as you realized already, for 命じる it could have been only order. 皿を洗いなさい/皿を洗え.
PS
I will revamp this lesson within this week to be more understandable!
Thanks for clarify and the fast fix!
Coincidentally, I have been asked during the review one of the sentence that you have just fixed.
Although the example it is correct: “Even though I had just finished cleaning the house, I was requested to do the dishes. [in such a way]” the review is asking me “Even though I had just finished cleaning the house, I requested to do the dishes. [in such a way]” as you can see the “was” is missing in the review.
Fixed! 
