hinlegen
to put down
To put something in a specific place, usually in a lying or flat position.
Du kannst die Post einfach auf den Küchentisch hinlegen.
You can simply put the mail down on the kitchen table.

to put down / to lie down
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to put down
To put something in a specific place, usually in a lying or flat position.
Du kannst die Post einfach auf den Küchentisch hinlegen.
You can simply put the mail down on the kitchen table.

'Hinlegen' (to put down / to lie down) is a separable verb. The prefix 'hin-' separates from the verb in main clauses and stands at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er legt das Buch auf den Tisch hin.
He puts the book down on the table.
The verb 'hinlegen' (to put down / to lie down) always needs an accusative object. This can be a thing, as in 'etwas hinlegen' (to put something down), or a reflexive pronoun, as in 'sich hinlegen' (to lie down).
Sie legt ihre Jacke auf das Sofa.
She puts her jacket on the sofa.
The reflexive form 'sich hinlegen' has two colloquial meanings. Whether it means 'sich ausruhen' (to rest) or 'hinfallen' (to fall down) can only be recognized from context. An intentional action suggests resting; an accident suggests falling down.
Ich bin so müde, ich lege mich kurz hin.
I'm so tired; I'm going to lie down for a moment.
In the colloquial meaning 'eine Leistung erbringen' (to deliver a performance), 'hinlegen' is often combined with nouns from the area of performance. Typical phrases are 'einen Auftritt' (a performance), 'eine tolle Show' (a great show), or 'eine super Prüfung' (a great exam) hinlegen.
Die junge Pianistin hat ein beeindruckendes Konzert hingelegt.
The young pianist pulled off an impressive concert.
When 'hinlegen' is used colloquially to mean 'bezahlen' (to pay), the price often stands as the accusative object. The preposition 'für' indicates what was paid for.
Für dieses alte Fahrrad soll ich 50 Euro hinlegen? Das ist zu viel.
I'm supposed to shell out 50 euros for this old bike? That's too much.
to lie / be located
'liegen' and 'hinlegen' can both have to do with a lying position, but they do not describe the same thing. 'Liegen' describes a state: a person or thing is already in a horizontal position. 'Hinlegen' describes a movement or action: someone brings something, or themselves, into this position. Learners often confuse the words because both appear in sentences with beds, sofas, tables, or floors. Remember: if something is already there, you say 'liegen'. If someone changes the position, you say 'hinlegen' or 'sich hinlegen'.

Nach dem Mittagessen legt sich Ali kurz aufs Sofa.
After lunch, Ali lies down on the sofa for a bit.
Das Buch liegt noch auf dem Küchentisch.
The book is still lying on the kitchen table.