लाइब्रेरियन को पुस्तकालय कार्ड दिखाइए और पत्रिका उधार लीजिए।

को marks the person the action is directed to. Here, लाइब्रेरियन को means to the librarian.

So the structure is:

• लाइब्रेरियन को = to the librarian
• पुस्तकालय कार्ड = library card
• दिखाइए = show

In other words: Show the library card to the librarian.

Hindi usually puts the verb at the end. English says:

Show the library card to the librarian

but Hindi naturally says something more like:

To the librarian the library card show

So in लाइब्रेरियन को पुस्तकालय कार्ड दिखाइए, the verb दिखाइए comes last. The same thing happens in the second part:

• पत्रिका उधार लीजिए = magazine borrow take

This verb-final order is very normal in Hindi.

Yes. पुस्तकालय कार्ड is a noun + noun combination, where the first noun describes the second.

• पुस्तकालय = library
• कार्ड = card

Together: library card

Hindi often uses this kind of compound structure, just like English does in phrases such as library card, school bus, or coffee cup.

Also, in everyday Hindi, many speakers might say लाइब्रेरी कार्ड instead. Both are understandable.

दिखाइए is a polite command form of दिखाना, which means to show.

So:

• दिखाना = to show
• दिखाइए = please show / show (polite)

This is the kind of form you use when speaking respectfully, usually to आप.

लीजिए is a polite command form of लेना, meaning to take.

So:

• लेना = to take
• लीजिए = please take / take (polite)

In this sentence, it combines with उधार to mean borrow:

• उधार लीजिए = borrow / take on loan

Like दिखाइए, this is a respectful आप-style command.

Hindi often expresses ideas with a noun or adverb-like word plus a verb. Here:

• उधार = on loan / borrowed
• लेना = to take

So उधार लेना literally means to take on loan, which is the normal way to say to borrow.

This is very natural Hindi. Many actions are expressed this way rather than with a single verb.

Because पत्रिका is the direct object, and in Hindi direct objects are often left unmarked, especially when they are inanimate.

Here:

• लाइब्रेरियन को = indirect object / recipient
• पत्रिका = direct object

Hindi often uses को with people, animate nouns, or very specific/emphasized direct objects, but not always with ordinary inanimate objects like पत्रिका.

So पत्रिका उधार लीजिए sounds normal.

Hindi does not normally use articles the way English does. There is no exact everyday equivalent of a/an/the that has to appear in sentences like this.

So Hindi can simply say:

• लाइब्रेरियन = the librarian / a librarian
• पत्रिका = the magazine / a magazine

The exact meaning depends on context. English needs articles; Hindi usually does not.

Not necessarily. The polite verb forms दिखाइए and लीजिए already make the sentence respectful.

So this sentence already sounds polite.

If you want to make it even more explicitly polite, you could add कृपया at the beginning:

कृपया लाइब्रेरियन को पुस्तकालय कार्ड दिखाइए और पत्रिका उधार लीजिए।

But it is not required.

Yes, this sentence is polite/respectful because it uses दिखाइए and लीजिए, which go with आप-style speech.

If you were speaking less formally to a friend, you might say something like:

लाइब्रेरियन को लाइब्रेरी कार्ड दिखाओ और पत्रिका उधार लो।

That is less polite and more casual.

So the original sentence is a good choice for instructions, public notices, or respectful speech.

Because modern Hindi mixes vocabulary from different sources very freely.

• पुस्तकालय is a more Sanskrit-based Hindi word for library
• लाइब्रेरियन is an English loanword adapted into Hindi

This kind of mixing is extremely common in real Hindi. In fact, many speakers would also say लाइब्रेरी instead of पुस्तकालय.

There is also a more formal Hindi word for librarian: पुस्तकालयाध्यक्ष, but in everyday usage लाइब्रेरियन is much more common.