ערכת התיקון מתחת לאוכף.

Hebrew usually leaves out the present-tense verb to be.

So:

• ערכת התיקון מתחת לאוכף
  literally looks like the repair kit under the saddle
• but it naturally means The repair kit is under the saddle

This is very normal in Hebrew. In the past or future, Hebrew would use an actual verb, for example:

• ערכת התיקון הייתה מתחת לאוכף = The repair kit was under the saddle
• ערכת התיקון תהיה מתחת לאוכף = The repair kit will be under the saddle

Because ערכת is the construct form of ערכה.

• ערכה = a kit
• ערכת ... = kit of ...

Hebrew often links two nouns this way. This structure is called סמיכות in Hebrew and construct state in English grammar.

So:

• ערכת התיקון literally = kit of the repair
• natural English = repair kit

A useful pattern to remember:

• many feminine nouns ending in ־ה change to ־ת in construct
• so ערכה becomes ערכת

In a construct chain, definiteness is usually shown on the last noun, and that makes the whole chain definite.

Compare:

• ערכת תיקון = a repair kit
• ערכת התיקון = the repair kit

So even though ערכה itself does not take ה־ here, the whole phrase becomes definite because תיקון is definite: התיקון.

That is a very common Hebrew pattern.

Because מתחת normally goes with ל־ before the noun:

• מתחת ל... = under ... / beneath ...

So:

• מתחת לאוכף = under the saddle / under a saddle depending on context

This is the standard modern Hebrew construction.
You generally would not say מתחת האוכף.

In normal unpointed Hebrew spelling, it can be ambiguous.

That is because:

• לְ + אוכף = to/under a saddle
• לָ + אוכף = to/under the saddle

But without vowel marks, both are written the same way: לאוכף.

So the exact meaning depends on context. If the meaning shown to the learner is under the saddle, that is perfectly possible here.

This ambiguity is especially common when a preposition attaches to a word beginning with א.

In everyday Modern Hebrew, מתחת ל־ is the usual way to say under / underneath / below.

• מתחת לשולחן = under the table
• מתחת לאוכף = under the saddle

תחת also exists, but it is often:

• more formal or literary
• less common in everyday speech for simple location
• sometimes used in other meanings depending on context

So for a learner, מתחת ל־ is the safer and more natural everyday pattern.

Not naturally in this case.

For a phrase like repair kit, Hebrew strongly prefers the construct state:

• ערכת תיקון = a repair kit
• ערכת התיקון = the repair kit

Using של here would sound awkward or unnatural:

• ערכה של תיקון is not how Hebrew normally says repair kit

Hebrew uses של more for regular possession or when a construct phrase would be too awkward or unclear.

So here, ערכת ... is the form you want.

Yes. This is a normal Hebrew order:

• ערכת התיקון = the subject
• מתחת לאוכף = the location

So the pattern is basically:

• [subject] + [place]

That is a very natural way to say The repair kit is under the saddle.

If you wanted a slightly fuller version, you could also say:

• ערכת התיקון נמצאת מתחת לאוכף

That means the same thing, but with נמצאת making the sentence more explicit.