बचपन की यह तस्वीर पुरानी है।

Here की is the possessive marker, similar to of or 's in English.

So बचपन की तस्वीर means something like:

• a picture of childhood
• a childhood picture
• a picture from childhood

In Hindi, this possessive marker comes after the first noun:

• बचपन की तस्वीर = childhood-of picture

It does not always mean literal ownership. It often shows a relationship, category, time, or association.

Because की / का / के change to agree with the noun that comes after them, not with बचपन.

The noun being described here is तस्वीर, and तस्वीर is:

• feminine
• singular

So the correct form is की.

Compare:

• बचपन की तस्वीर = a childhood picture (तस्वीर is feminine)
• बचपन का फोटो = a childhood photo (फोटो is usually treated as masculine)
• बचपन के दिन = childhood days (दिन is plural)

This agreement pattern is very important in Hindi.

Because पुरानी agrees with तस्वीर, which is feminine singular.

The basic adjective is पुराना = old.
It changes like this:

• पुराना for masculine singular
• पुरानी for feminine singular
• पुराने for masculine plural (and some other contexts)

Since तस्वीर is feminine, we get:

• पुरानी तस्वीर
• तस्वीर पुरानी है

So the -ी ending is there because of grammatical gender agreement.

Because in this sentence पुरानी is being used as a predicate adjective, not directly as part of the noun phrase.

Hindi structure here is:

• तस्वीर पुरानी है
• literally: the picture old is

This is like saying The picture is old.

If you wanted old directly before the noun, you could say:

• पुरानी तस्वीर = old picture

So compare:

• यह तस्वीर पुरानी है = This picture is old
• यह पुरानी तस्वीर है = This is an old picture

Both are correct, but they mean slightly different things.

यह means this.

So:

• यह तस्वीर = this picture

It points to something near the speaker, just like English this.

You may also hear it pronounced more like ये in everyday speech, but in writing the standard singular form is यह.

है is the present-tense form of to be for a singular subject.

So:

• तस्वीर पुरानी है = The picture is old

Because तस्वीर is singular, we use है.

If the subject were plural, Hindi would usually use हैं:

• ये तस्वीरें पुरानी हैं = These pictures are old

Usually it means a picture from childhood or a childhood picture.

In natural English, that is probably the best interpretation.

Literally, बचपन की तस्वीर could look like picture of childhood, but in normal usage it often refers to a picture associated with someone’s childhood period.

So if someone shows an old photo and says this sentence, they usually mean:

• This childhood picture is old
• or more naturally, This picture from childhood is old

Hindi normally does not use articles like English a, an, and the.

So यह तस्वीर can mean:

• this picture

and तस्वीर by itself can mean:

• a picture
• the picture

The exact meaning depends on context.

That is very normal in Hindi. You usually understand definiteness from the situation, word order, or demonstratives like यह and वह.

Yes, to some extent. Hindi word order is flexible, but not completely free. Different orders can sound more natural in different contexts.

For example:

• बचपन की यह तस्वीर पुरानी है।
  = This childhood picture is old.

You could also say:

• यह बचपन की तस्वीर पुरानी है।

That is also understandable and natural in many contexts.

But if you say:

• यह पुरानी बचपन की तस्वीर है।

that changes the structure and means more like:

• This is an old childhood picture.

So the placement of words can affect what is being emphasized and whether old is part of the noun phrase or part of the statement.

It does not matter here in the way many learners expect.

Even though nouns have gender in Hindi, in the phrase बचपन की तस्वीर, the form की is chosen because of तस्वीर, not because of बचपन.

That is a common point of confusion for English speakers.

So in possessive-type constructions like this:

• X का/की/के Y

the का/की/के agrees with Y, the noun after it.

Here:

• X = बचपन
• Y = तस्वीर

Since तस्वीर is feminine singular, we use की.

No, that would be incorrect in standard Hindi.

Because तस्वीर is feminine singular, the possessive marker must be की, not का.

So the correct form is:

• बचपन की यह तस्वीर

A useful shortcut is: look at the noun after का/की/के.

If it is:

• masculine singular -> का
• feminine singular -> की
• plural -> के

The pattern is:

• [descriptive phrase] + [subject] + [adjective] + है

More specifically:

• बचपन की = related to childhood
• यह तस्वीर = this picture
• पुरानी = old
• है = is

So the full structure is:

• बचपन की यह तस्वीर पुरानी है।
• literally: Childhood-related this picture old is.

A natural English rendering would be:

• This childhood picture is old.
• or This picture from childhood is old.

This is a very common Hindi sentence pattern:
noun + adjective + है

For example:

• घर बड़ा है। = The house is big.
• किताब नई है। = The book is new.
• तस्वीर पुरानी है। = The picture is old.