だけしか is a combination of two 副助詞（ふくじょし） (adverbial particles), だけ ‘only’, and しか ‘nothing but’. This structure primarily follows nouns, before part (B) of the sentence will have a corresponding ない based word.
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彼（かれ）は野菜（やさい）だけしか食（た）べれません。
He can only eat vegetables.
土曜日（どようび）だけしか忙（いそが）しくないから、出来（でき）たら土曜日（どようび）がいい。
Only Saturdays aren't busy, so if possible Saturday is preferable.
この中（なか）ではタケシだけしか上手（じょうず）ではない。他（ほか）はみんな結構（けっこう）うまい。
In this group, Takeshi is the only one that isn't good. Everyone else is considerably skilled.
何（なん）でこのコップだけしか500円（えん）ではないの？
Why is this cup the only one that isn't 500yen?
Despite all of these possibilities, it should be noted that だけしか～ない is an expression that appears with negative verbs, far more than any of the other combinations.
だけしか may appear as though it is saying ‘only’ twice, but each particle has its own specific nuance. These nuances are as follows:
だけ - Removes one thing (from within a group), and presents it as the ‘only’ thing that fits a certain criteria.
しか - Highlights something that exists by itself as not having any alternatives.
Due to this, each meaning compounds together, with だけ saying ‘just this’, while しか adds ‘and only this!’. Reversing the order and putting しか before だけ would not work, as the sequence of selection needs to be logical.
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日曜日（にちようび）しかだけ休（やすみ）みが取（と）れない。 (Unnatural)
I can take only breaks on Sunday.
日曜日（にちようび）だけしか休（やす）みが取（と）れない。 (Natural)
I can only take breaks on Sunday.