Der Klebestift liegt neben den Buntstiften auf dem Tisch.

Because Klebestift is the subject of the sentence, so it is in the nominative case.

• der Klebestift = the glue stick (nominative)
• den Klebestift = the glue stick (accusative)
• dem Klebestift = to / for the glue stick (dative)

In this sentence, the glue stick is the thing doing the action of liegen (to lie / to be lying), so German uses the nominative:

• Der Klebestift liegt ... = The glue stick is lying / is located ...

Klebestift is a compound noun:

• kleben = to glue / stick
• Stift = stick, pen, pencil, crayon, or a stick-shaped item

So Klebestift means glue stick.

German often builds nouns this way by combining smaller words into one longer word.

German often prefers position verbs where English often just uses is.

• liegen = to lie, to be lying, to be located horizontally
• stehen = to stand, to be standing
• sitzen = to sit, to be sitting

So:

• Der Klebestift liegt auf dem Tisch. = The glue stick is on the table.

A glue stick is thought of as lying rather than standing, so liegt sounds natural.

You could sometimes translate it simply as is, but the German verb gives a more physical sense of position.

Because neben is a two-way preposition. That means it can take either:

• accusative for movement toward a place
• dative for location in a place

Here, the sentence describes where the glue stick is, not movement. So German uses the dative.

Since Buntstiften is plural, the dative plural article is den:

• neben den Buntstiften = next to the colored pencils

Compare:

• Der Klebestift liegt neben den Buntstiften. = It is next to them. (location → dative)
• Ich lege den Klebestift neben die Buntstifte. = I put the glue stick next to the colored pencils. (movement/direction → accusative)

Great question: den can mean more than one thing in German.

Here it is not masculine accusative. It is dative plural.

German articles can look the same in different cases. In this sentence:

• die Buntstifte = the colored pencils (nominative/accusative plural)
• den Buntstiften = the colored pencils (dative plural)

You can tell it is dative plural because:

1. neben is describing location, so it needs dative
2. the noun has the extra -n ending: Buntstiften

Because in the dative plural, German nouns usually add -n if they do not already end in -n or -s.

So:

• die Buntstifte = the colored pencils
• den Buntstiften = to/with/next to the colored pencils

This extra -n is very common in dative plural:

• mit den Kindern
• bei den Freunden
• neben den Buntstiften

This is the same location-vs-movement pattern.

• auf dem Tisch = on the table (location, dative)
• auf den Tisch = onto the table (direction/movement, accusative)

In your sentence:

• Der Klebestift liegt ... auf dem Tisch.
  • The glue stick is already there.
  • So German uses dative.

Compare:

• Ich lege den Klebestift auf den Tisch.
  • I put the glue stick onto the table.
  • That is movement toward a place, so German uses accusative.

Because they give two different pieces of location information:

• neben den Buntstiften = next to the colored pencils
• auf dem Tisch = on the table

So the sentence tells you both:

1. the glue stick is on the table
2. and more specifically, it is next to the colored pencils

English works the same way:

• The glue stick is next to the colored pencils on the table.

Yes, it often can.

For example:

• Der Klebestift liegt neben den Buntstiften auf dem Tisch.
• Der Klebestift liegt auf dem Tisch neben den Buntstiften.

Both are natural. The difference is mostly about focus or what feels more important in the moment.

A rough idea:

• neben den Buntstiften auf dem Tisch can emphasize the glue stick’s relation to the pencils first
• auf dem Tisch neben den Buntstiften can present the table as the main location first

Both are grammatically fine.

The basic singular noun is der Buntstift, which means colored pencil.

Forms:

• der Buntstift = the colored pencil
• die Buntstifte = the colored pencils
• den Buntstiften = the colored pencils (dative plural)

Like Klebestift, this is also a compound noun:

• bunt = colorful
• Stift = pencil / pen / stick-like writing tool

So Buntstift literally means something like color-pencil.

In German, all nouns are capitalized, not just proper names.

So:

• der Klebestift
• die Buntstifte
• der Tisch

This is a normal rule in German writing and helps learners spot nouns more easily.

A simple pronunciation guide is:

Der KLE-be-shtift leekt NAY-ben den BUNT-shtif-ten owf dem tish.

A few helpful notes:

• ie in liegt sounds like a long ee
• st at the beginning of a syllable often sounds like sht
  • Stift sounds like shtift
• z in German sounds like ts, though there is no z in this sentence
• auf sounds roughly like owf

If you want to sound natural, stress the main content words:

• Der KLEbestift liegt NÉben den BÚNTstiften auf dem TÍsch.