Я не могу представить себе сад без ярких цветов.

Breakdown of Я не могу представить себе сад без ярких цветов.

я
I
не
not
яркий
bright
цветок
the flower
сад
the garden
мочь
to be able
без
without
представить себе
to imagine
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Questions & Answers about Я не могу представить себе сад без ярких цветов.

Can you give a literal, word-for-word breakdown of Я не могу представить себе сад без ярких цветов?

Я – I
не – not
могу – can / am able to
представить – (perfective infinitive) to imagine
себе – to myself
сад – garden (accusative; inanimate masculine stays the same)
без – without
ярких – bright (genitive plural of яркий)
цветов – flowers (genitive plural of цветок)

Put together it literally reads: “I not can imagine to myself garden without bright flowers,” i.e. “I can’t imagine a garden without bright flowers.”

Why is себе used after представить?
The verb представить (to imagine) normally takes a dative object to indicate who is doing the imagining. You ask представить кому? (“to imagine to whom?”). Here себе is the dative form of “myself,” so it literally means “to imagine to myself.” Omitting себе isn’t grammatically wrong (“Я не могу представить сад…”), but including it is the most natural way to say “I can’t imagine.”
Why does сад look the same in this sentence as it does in the dictionary (nominative) form?
Сад is an inanimate masculine noun. In Russian, the accusative singular of inanimate masc. nouns is identical to the nominative. Since представить takes a direct object in the accusative, сад remains unchanged.
Why are ярких and цветов in the genitive plural?

The preposition без (“without”) always requires the genitive case. Because цветы is plural, you use the genitive plural for both the noun and its adjective:
ярких is genitive plural of яркий (“bright”)
цветов is genitive plural of цветок (“flower”)

Could I say Я не могу представить себе сад без яркие цветы instead?
No. Because of без, both adjective and noun must be genitive plural. Яркие цветы is nominative plural; the correct genitive plural form is ярких цветов.
Why is представить perfective? Could I use the imperfective представлять here?
Using the perfective представить focuses on the completed result (“to form the image” in one go). In modal constructions with мочь/не могу, choosing perfective suggests the speaker is unable to achieve that full, one-time mental result. The imperfective не могу представлять себе… would emphasize an ongoing inability to picture it over time, which is less common in this context.
Are there synonyms for представить себе? How about вообразить?

Yes.
вообразить себе (perfective) / воображать себе (imperfective) also mean “to imagine.”
вообразить can sound a bit more formal or literary.
In everyday speech, представить себе is more common.

How would I say “my garden” instead of just “garden”?

You can use the possessive pronoun свой (reflexive) when it refers back to the subject:
Я не могу представить себе свой сад без ярких цветов.
You could also say мой сад, but свой сад is stylistically preferred when the owner is the subject of the sentence.

Where are the stresses in Я не могу представить себе сад без ярких цветов?

Я не мо́гу предста́вить се́бе сад без я́рких цве́тов
мо́гу (second syllable)
предста́вить (second syllable)
се́бе (first syllable)
я́рких (first syllable)
цве́тов (second syllable)

Why aren’t there any articles (a/the) in Russian? How do I know if it’s “a garden” or “the garden”?
Russian doesn’t use articles like a or the. Context tells you whether a noun is definite or indefinite. In this sentence, сад simply means “a garden” in general. If you need to emphasize particularity, you might add words like этот сад (“this garden”) or любой сад (“any garden”).