You can think of it like this :

At first
Denzer ⬛ + 21
Nora ⬛

We pretend that he gives all those 21 bookmarks to Nora first.

①Denzer gives 21 to Nora.

Now

Denzer ⬛
Nora ⬛ + 21

We see that it's like they basically switch around. At first Denzer got 21 more, now Nora has 21 more.

② But now Nora has too many. She is only supposed to have 11 more than Denzer.

So she needs to give back some to Denzer.

Now 21 - 11 = 10

So their difference must be decreased by 10.

How to give? Nora must give half of that difference back to Denzer.

10 ÷ 2 = 5

She will have 5 less, Denzer will gain 5 more.


So, in the end,


Nora
⬛ + 21 - 5 , which is equal to
⬛ + 16

Denzer
⬛ + 5

The difference now is 11. It is correct.


Since Nora got 16 more than at first, Denzel gave Nora 16 bookmarks.

In summary, the steps are :


21 - 11 = 10
10 ÷ 2 = 5
5 + 11 = 16

Alternative method:

Find the difference between the bookmarks each person has at first and in the end.

At first,

Denzer has 21 more. Nora has 21 less.

In the end,

Nora has 11 more. Which means Denzer has 11 less.

21 + 11 = 32

His difference with Nora dropped by 32.


How does this occur?

Denzer must have given half of that difference to Nora.

32 ÷ 2 = 16

Denzer gave away 16, so he has 16 less now, so the difference decreases by 16.

That 16 goes to Nora, who has 16 more now, the difference decreases by another 16.

The concept is that the difference always changes by twice the amount transferred.


Simpler example :

At first,
Denzer : $20
Nora : $15

Difference: $20 - $15 = $5


Let's say Denzer gives Nora $2.

Denzer now : $20 - $2 = $18
Nora now : $15 + $2 = $17

Difference now = $18 - $17 = $1

Change in difference = $5 - $1 = $4

Notice that $4 is twice of the $2 that was transferred to the other person.

Another example (but with position change)

At first,

Denzer : $20
Nora : $15

Difference: $20 - $15 = $5

Let's say Denzer gives Nora $8.

Denzer now : $20 - $8 = $12
Nora now : $15 + $8 = $23

Difference now = $23 - $12 = $11

Now the position has changed. At first Denzer has $5 more. Now he is the one that has less. He has $11 less now.


Change in difference = $5 + $11 = $16

From $5 more to $11 less, that's a change/gap of $16

(Now you haven't learnt negative numbers but this is how it would be represented

+$5
↓-$16
-$11

Notice that $16 is twice of the $8 that was transferred.