Hon är duktig på att planera.

Both can often translate to good, but they are not used in exactly the same way.

• duktig usually describes a person's skill, ability, or competence
• bra is more general and can mean good, fine, well

In Hon är duktig på att planera, duktig means she is skilled at planning.

Compare:

• Hon är duktig på att planera. = She is skilled at planning.
• Planen är bra. = The plan is good.

So duktig is the more natural choice when talking about what someone is good at doing.

In this sentence, på is part of the fixed expression duktig på, which means good at or skilled at.

So:

• duktig på något = good at something
• duktig på att göra något = good at doing something

Examples:

• Hon är duktig på matte. = She is good at math.
• Han är duktig på att laga mat. = He is good at cooking.

Even though på often means on in other contexts, here you should think of duktig på as a chunk meaning good at.

Because att is the infinitive marker, like to in English.

• att planera = to plan
• att läsa = to read
• att skriva = to write

So:

• Hon är duktig på att planera. = She is good at planning / She is good at how to plan

After duktig på, if you want to say someone is good at doing something, Swedish commonly uses:

• duktig på att + infinitive

Example:

• Jag är duktig på att organisera. = I am good at organizing.

Yes, you might see similar noun-based structures, but Hon är duktig på att planera is the more natural everyday way to say She is good at planning.

Compare:

• duktig på att planera = good at planning (focusing on the action)
• duktig på planering = good at planning/planning work (more abstract or formal-sounding)

Learners should usually start with:

• duktig på att + verb

because it is very common and easy to build with many verbs.

This is the normal Swedish main-clause word order:

• subject + verb + complement

So:

• Hon = subject
• är = verb
• duktig på att planera = complement

This is very similar to English:

• She is good at planning.

Swedish main clauses usually put the finite verb in the second position, and here that gives:

• Hon är ...

är is the present tense of vara, which means to be.

Forms of vara:

• är = is / am / are (present)
• var = was / were
• varit = been

So:

• Jag är = I am
• Du är = You are
• Hon är = She is

In this sentence, Hon är simply means She is.

Yes, adjectives in Swedish can change form, but here duktig is in its common singular form, which matches hon.

Some basic patterns:

• en-word/common singular: duktig
• ett-word/neuter singular: duktigt
• plural: duktiga

Examples:

• Hon är duktig. = She is skilled.
• Barnet är duktigt. = The child is well-behaved / skilled.
• De är duktiga. = They are skilled.

In your sentence, hon takes duktig.

Yes, duktig can mean different things depending on context.

Common meanings include:

• skilled / capable
• good at something
• well-behaved (especially about children)
• sometimes hard-working

In Hon är duktig på att planera, the context clearly shows the skilled/capable meaning.

Compare:

• Hon är duktig på att planera. = She is good at planning.
• Barnet är duktigt. = The child is well-behaved.

So the phrase after it often helps you understand which meaning is intended.

Not naturally. A word-for-word translation would sound strange in English.

A better natural translation is:

• She is good at planning
• She is skilled at planning

This is a useful reminder that Swedish expressions often do not match English word-for-word:

• duktig på = good at
• att planera = to plan

So it is better to learn the whole pattern:

• vara duktig på att + verb

You just change the subject, and sometimes the adjective form if needed.

Examples:

• Jag är duktig på att planera. = I am good at planning.
• Du är duktig på att planera. = You are good at planning.
• Han är duktig på att planera. = He is good at planning.
• Vi är duktiga på att planera. = We are good at planning.
• De är duktiga på att planera. = They are good at planning.

Notice:

• singular person here: duktig
• plural: duktiga

Yes, planera is a common verb meaning to plan.

A rough pronunciation guide is:

• pla-ne-RA
• the stress is on the last syllable: -ra

This is common for many Swedish verbs ending in -era, such as:

• studera = study
• organisera = organize
• diskutera = discuss

So planera is a useful verb to learn early.

Yes, but it means something slightly different in emphasis.

• Hon är duktig på att planera. = She is good at planning.
  Focus: her general ability or skill.
• Hon planerar bra. = She plans well.
  Focus: the way she performs the action.

Both are possible, but är duktig på att planera sounds more like a statement about her competence in general.