This is the 99th most frequent Japanese word.
しれ
The word "しれ" can mean "know" or "be aware" (imperative form of 知る [shiru]).
In this sentence, 'しれ' is part of the form 'しれない', which implies an inability to understand or grasp.
どうすればいいか、分かりしれない。
It is hard to comprehend what should be done.
Here, 'しれない' is used to express something that cannot be measured or estimated.
彼の能力は計りしれない。
His abilities are beyond measure.
In this example, 'しれない' indicates difficulty or impossibility in obtaining understanding or knowledge.