मेरी बहन जल्दी हिंदी सीख सकती है।

A word-by-word breakdown is:

• मेरी = my
• बहन = sister
• जल्दी = quickly / soon
• हिंदी = Hindi
• सीख = learn (verb stem)
• सकती है = can / is able to (feminine singular)

So the whole sentence means something like My sister can learn Hindi quickly.

Because बहन (sister) is a feminine singular noun.

In Hindi, possessive words like मेरा / मेरी / मेरे agree with the noun being possessed, not with the possessor.

So:

• मेरा भाई = my brother
• मेरी बहन = my sister
• मेरे दोस्त = my friends / my male friend in some contexts depending on structure

Here, since बहन is feminine singular, you use मेरी.

Because the subject बहन is feminine singular.

In a sentence with सकना (to be able to / can), the form of सकना agrees with the subject:

• वह सीख सकता है = He can learn
• वह सीख सकती है = She can learn
• वे सीख सकते हैं = They can learn

So in मेरी बहन जल्दी हिंदी सीख सकती है, सकती matches बहन.

This is a very common Hindi structure:

main verb stem + सकना + होना

Here:

• सीख = verb stem of सीखना (to learn)
• सकती = feminine singular form of सकना (can / be able to)
• है = is

So:

• सीख सकती है literally = is able to learn
• natural English = can learn

This is how Hindi often expresses can.

Because Hindi usually follows Subject–Object–Verb word order.

English:

• My sister can learn Hindi quickly

Hindi:

• मेरी बहन जल्दी हिंदी सीख सकती है
• literally: My sister quickly Hindi learn can

In Hindi, the verb normally comes at the end, and the object (हिंदी) comes before the verb.

Here जल्दी means quickly.

So जल्दी हिंदी सीख सकती है means can learn Hindi quickly.

But जल्दी can also mean soon in other contexts. For example:

• मैं जल्दी आऊँगा। = I will come soon.

So the exact meaning depends on context.

Yes, Hindi word order is somewhat flexible, especially with adverbs like जल्दी.

These can all be natural, though the emphasis may change slightly:

• मेरी बहन जल्दी हिंदी सीख सकती है।
• मेरी बहन हिंदी जल्दी सीख सकती है।

Both mean roughly My sister can learn Hindi quickly.

The version you have is completely normal.

Hindi does not need a separate word like English to in this structure.

English says:

• She is able to learn

Hindi says:

• वह सीख सकती है

The verb stem सीख is used directly before सकना. So Hindi expresses the idea differently from English.

Yes. हिंदी is what is being learned, so it is the object.

Compare:

• वह हिंदी सीखती है। = She learns Hindi.
• वह हिंदी सीख सकती है। = She can learn Hindi.

The object stays before the verb, which is normal in Hindi.

Hindi does not use articles the way English does.

English often requires:

• a sister
• the language
• the Hindi language

Hindi usually does not have words that directly match a/an/the in normal sentences. So मेरी बहन simply means my sister, and हिंदी simply means Hindi.

You would change the agreeing words to masculine forms.

For example:

• मेरा भाई जल्दी हिंदी सीख सकता है।
• My brother can learn Hindi quickly.

Changes:

• मेरी → मेरा because भाई is masculine singular
• सकती → सकता because the subject is masculine singular

For a plural feminine subject, you would use plural agreement:

• मेरी बहनें जल्दी हिंदी सीख सकती हैं।
• My sisters can learn Hindi quickly.

Changes:

• बहन → बहनें = sisters
• है → हैं for plural
• सकती often stays सकती with feminine plural subjects in this construction, while plurality is shown by हैं and the noun

For masculine or mixed plural:

• मेरे भाई जल्दी हिंदी सीख सकते हैं।
• My brothers can learn Hindi quickly.

Normally, सकती है means can / is able to, not may in the sense of permission or possibility.

So the most natural meaning is:

• My sister can learn Hindi quickly
• My sister is able to learn Hindi quickly

It does not usually mean permission, like My sister may learn Hindi.

The dictionary form is सीखना, which means to learn.

In the sentence, you see the stem सीख because Hindi often uses the verb stem before another helping/modal verb:

• सीखना = to learn
• सीख सकती है = can learn

This pattern appears with many verbs:

• करना → कर सकता है = can do
• जाना → जा सकती है = can go
• लिखना → लिख सकते हैं = can write

Yes, it is natural and grammatical.

A native speaker would understand it clearly as:

• My sister can learn Hindi quickly

A slightly different but equally natural order is:

• मेरी बहन हिंदी जल्दी सीख सकती है।

Both are fine; the difference is mostly about flow or emphasis, not basic meaning.