If $[4.5]=[4+0.5]=4$, then $[-4.5]$ will be:

The notation $[x]$ denotes the greatest integer function (also known as the floor function), which returns the greatest integer less than or equal to $x$.
For a positive number like $4.5$:

$$\text{Integers less than or equal to }4.5\text{ are }\dots ,2,3,4.$$

The greatest among these is $4$. Thus, $[4.5]=4$.

For a negative number like $-4.5$:

$$\text{Integers less than or equal to }-4.5\text{ are }-5,-6,-7,\dots$$

The greatest among these integers is $-5$.

Alternatively, we can express $-4.5$ as:

$$-4.5=-5+0.5$$

Taking the floor value:

$$[-4.5]=-5$$