It seems you're not interpreting the sentence quite correctly.
It should be "As a child I had no way of knowing how my mother felt at that time."
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Would be "how my mother felt at the time."
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I think this is where you might be getting thrown off. `` is what you need to focus on. is the "child version" of the speaker, from that point in time. is saying that the preceding is not comprehensible _to_ him/her. I assume is the target grammar point so you should know that it's saying, basically, "had no way of knowing."