Learn Hardcore Swedish: Hon säger att hans gröna skjorta inte passar ihop med den gula slipsen. - She says that his green shirt does not go together with the yellow tie.

Unlike English, Swedish usually keeps att in this kind of sentence. Leaving it out is possible in some very informal speech, but for a learner you should treat att as required here.

So:

Correct: Hon säger att hans gröna skjorta inte passar ihop med den gula slipsen.
Avoid (especially in writing): Hon säger hans gröna skjorta inte passar…

Why is it hans and not sin in att hans gröna skjorta…?

Swedish distinguishes between:

hans = his (non‑reflexive, refers to some male person)
sin/sitt/sina = his/her/their own (reflexive, refers back to the subject of the same clause)

In your sentence:

Main clause subject: hon (she)
Subordinate clause: att hans gröna skjorta…
- Here the subject is hans gröna skjorta (or just skjorta if you strip modifiers).

Because hon is not the subject of the att‑clause, you cannot use sin to refer back to her. So you must use hans to indicate that the shirt belongs to some man.

Compare:

Han säger att hans gröna skjorta… = He says that his (some man’s, maybe him, maybe another guy’s) green shirt…
Han säger att sin gröna skjorta… = He says that his own green shirt… (here sin refers back to han, the subject of the same clause)

In your original sentence, hon is in a different clause, so only hans works.

Why is it gröna skjorta and not grön skjorta?

Without a possessive:

en grön skjorta = a green shirt (indefinite)
den gröna skjortan = the green shirt (definite)

With a possessive (hans/hennes/min/din etc.), Swedish treats the noun as definite, and then:

The noun itself is indefinite form: skjorta
The adjective takes the -a ending: gröna

So:

hans gröna skjorta
min blåa bil (my blue car)
deras stora hund (their big dog)

You almost never say hans grön skjorta; it’s ungrammatical.

Why is inte before the verb: att hans gröna skjorta inte passar ihop… and not passar inte?

Swedish word order changes in subordinate clauses (after att, som, eftersom, etc.).

In main clauses, the verb is in second position, so the pattern is typically:
- Subject – Verb – inte:
  Skjortan passar inte ihop med slipsen.
In subordinate clauses, inte comes before the finite verb:
- Subject – inte – Verb:
  …att skjortan inte passar ihop med slipsen.

Your sentence has a subordinate clause introduced by att, so the correct order is:

att hans gröna skjorta inte passar ihop med den gula slipsen
(not att hans gröna skjorta passar inte ihop…)

What does passar ihop med mean exactly, and how is it different from just passar?

Both are based on passa:

passa can mean:
- to fit (size, situation)
  - Byxorna passar. = The trousers fit.
- to suit (look good on someone)
  - Den färgen passar dig. = That color suits you.
passa ihop (med) means “to go together / to match (with)”:
- Skjortan passar ihop med slipsen.
  = The shirt goes well with the tie (they match in style/color).

In clothing/colour combination contexts, passar ihop or passar ihop med is the natural phrase.
If you only say passar med, it’s understandable, but passar ihop (med) is more idiomatic here.

Why is it den gula slipsen and not det gula slipsen?

Nouns in Swedish belong to one of two genders:

en‑words (common gender) → take den in definite form with an adjective
ett‑words (neuter) → take det

slips is an en‑word:

en slips = a tie
slipsen = the tie
with adjective: den gula slipsen = the yellow tie

If it were an ett‑word, you would have ett hus → det stora huset.

So:

den gula slipsen = correct
det gula slipsen = wrong, because slips is not an ett‑word.

Why do we need both den and -en in den gula slipsen? Isn’t that “double definite”?

Yes, Swedish uses so‑called double definiteness when an adjective comes before a definite noun.

Pattern:

Definite article (den/det/de)
Adjective with -a ending
Noun with definite ending (-en/-et/-na)

Examples:

den gula slipsen = the yellow tie
det stora huset = the big house
de röda bilarna = the red cars

You normally must have both elements.
Saying only gula slipsen without den is generally incorrect in standard Swedish.

Why is the verb passar in present tense here? Is it about the current moment only?

Swedish present tense is used for:

actions happening now
general truths / general statements

Here, it’s a kind of general judgement:

hans gröna skjorta inte passar ihop med den gula slipsen
= his green shirt doesn’t (generally) go well with the yellow tie.

English also uses present for this kind of general assessment:
“She says his green shirt doesn’t go with the yellow tie.”

So passar is the normal choice; you wouldn’t use past tense unless you were talking about some specific past situation with a time frame.

Could we drop ihop med and just say inte passar den gula slipsen?

Not really, that would sound wrong or at least very odd.

passa (någon/något) usually means “fit/suit (someone/something)”:
- Skjortan passar honom. = The shirt fits/suits him.

If you say:

Skjortan passar slipsen.

it sounds like the shirt fits the tie in a size/functional sense, which is strange.

To express that two items match in style or colour, you normally say:

passar ihop (med):
Skjortan passar inte ihop med slipsen.

So in your sentence, ihop med is doing important work: it changes the meaning from “fit/suit (someone)” to “go together / match (with)”.

Is there any difference between ihop med and tillsammans med here?

Both can literally mean together with, but in this clothing/colour context:

passar ihop med = natural, idiomatic (“goes together with / matches with”)
passar tillsammans med = understandable but less idiomatic and a bit heavier.

You will most often hear:

passar ihop med
or sometimes passar bra med

So stick with passar ihop med for talking about matching clothes or colours.