undougutu to hiyokebousi wo zyunbisuru.

A natural reading is:

うんどうぐつ と ひよけぼうし を じゅんびする。

• 運動靴（うんどうぐつ） = athletic shoes, sneakers
• と = and
• 日よけ帽子（ひよけぼうし） = sun hat / hat for blocking the sun
• を = object marker
• 準備する（じゅんびする） = to prepare

They do different jobs:

• と connects nouns: 運動靴 と 日よけ帽子 = athletic shoes and a sun hat
• を marks the thing being acted on by the verb:
  運動靴と日よけ帽子を = the athletic shoes and sun hat as the things being prepared

So the structure is:

[item A] と [item B] を 準備する
= prepare item A and item B

Japanese often leaves out the subject when it is understood from context.

So 運動靴と日よけ帽子を準備する could mean:

• I will prepare athletic shoes and a sun hat
• Prepare athletic shoes and a sun hat
• You should prepare athletic shoes and a sun hat

Which one it means depends on the situation.
In a checklist, instructions, or school notice, it often feels like Prepare/bring athletic shoes and a sun hat.

準備する is the plain/dictionary form.

This form is common in:

• written instructions
• notes
• headings
• checklist-style language
• casual speech

Compare:

• 準備する = plain, neutral, concise
• 準備します = polite
• 準備してください = please prepare
• 準備しましょう = let’s prepare

In short, 準備する often appears in short written directions because it is compact and neutral.

It literally means to prepare, but in context it can overlap with English ideas like:

• prepare
• get ready
• have ready
• sometimes even bring (depending on the situation)

For example, if this is on a school trip notice, the practical meaning may be closer to:

• Bring sneakers and a sun hat
• Have sneakers and a sun hat ready

Japanese often uses 準備する where English might choose a more specific verb based on context.

運動靴（うんどうぐつ） means athletic shoes, gym shoes, or sneakers.

It is more specific than just 靴（くつ）, which simply means shoes.

So:

• 靴 = shoes
• 運動靴 = sports shoes / sneakers

This word suggests shoes suitable for movement, exercise, or outdoor activity.

日よけ帽子（ひよけぼうし） is a hat that protects you from the sun.

Breakdown:

• 日（ひ） = sun, sunlight
• よけ = protection from / avoiding / shielding
• 帽子（ぼうし） = hat

So it is literally something like sun-shielding hat.

In natural English, you might say:

• sun hat
• hat for sun protection

In Japanese, 日 often means sunlight or the sun’s rays, especially in practical words related to shade or exposure.

So:

• 日よけ = sunshade / protection from sunlight

This is a very natural expression in Japanese.
Using 太陽 would sound less natural here, because 太陽 refers more directly to the sun as an object, while 日 often fits everyday expressions about sunshine and exposure better.

It is best understood as a compound noun:

• 日よけ = sun protection / sunshade
• 帽子 = hat

Together: 日よけ帽子 = sun hat

Japanese often combines nouns this way to make a more specific noun.

Yes, but Japanese often omits punctuation in short simple phrases.

You might also see:

• 運動靴と日よけ帽子を準備する。
• 運動靴、日よけ帽子を準備する。
• 運動靴と日よけ帽子を準備してください。

The version without spaces is the normal Japanese way of writing it:

運動靴と日よけ帽子を準備する。

The spaces in your example are probably there just to help learners read it.

Japanese nouns usually do not mark singular vs. plural the way English does.

So:

• 運動靴 can mean athletic shoes in a general sense, and in practice usually implies a pair
• 日よけ帽子 can mean a sun hat or sun hats, depending on context

Usually context tells you what is meant. In a packing instruction, English naturally translates this as:

• Prepare sneakers and a sun hat

Even though Japanese does not explicitly mark a pair of sneakers or one hat.

Yes, but the meaning changes slightly.

• と = a complete, definite list
  運動靴と日よけ帽子 = athletic shoes and a sun hat
• や = examples, an incomplete list
  運動靴や日よけ帽子 = things like athletic shoes and sun hats

So in a direct instruction about exactly what to prepare, と is the better choice.

Not grammatically, no. It is in the plain non-past form, not a direct command form.

However, in context, it can function like an instruction.

Compare:

• 準備する。 = prepare / will prepare / to prepare, depending on context
• 準備しろ。 = prepare! very direct, blunt command
• 準備してください。 = please prepare

So this sentence is not a harsh command, but in a notice or checklist it can still have an instructional feel.

The structure is:

[noun] と [noun] を [verb]

More specifically:

• 運動靴と日よけ帽子 = the two items
• を = marks them as the object
• 準備する = the action

So the sentence pattern is:

A と B を 準備する。
= Prepare A and B.

This is a very useful pattern you can reuse with other nouns.