“At most” means “less than or equal to”.
The question is to find n where:
4≤¾(n+20),
Multiplying both sides by 4:
16≤3(n+20),
16≤3n+60,
Subtracting 60 from each side:
-44≤3n,
-44/3≤n which is the same as:
n≥-44/3.
This means any number greater than or equal to (more positive than) to -44/3.
Let’s pick an example: n=-42/3=-14.
Check if the inequality is true:
Is 4≤¾(-14+20)?
20-14=6, and ¾ of 6 is 4½.
It is true that 4 is less than 4½, so n is at least -44/3 or -14⅔.