#### Answer

a) natural numbers: $\{
\sqrt{4}
\}
$
b) whole numbers: $\{
0,\sqrt{4}
\}
$
c) integers: $\{
-6,0,\sqrt{4}
\}
$
d) rational numbers: $\{
-6,0,0.\overline{7},\sqrt{4}
\}
$
e) irrational numbers: $\{
-\pi,\sqrt{3}
\}
$
f) real numbers: $\{
-6,-\pi,0,0.\overline{7},\sqrt{3},\sqrt{4}
\}
$

#### Work Step by Step

a) Natural numbers include the numbers $\{1,2,3,4,...\}.$ Hence, from the given set, the natural number is
\begin{array}{l}\require{cancel}
\{
\sqrt{4}
\}
.\end{array}
b) Whole numbers include the numbers $\{0, 1,2,3,4,...\}.$ Hence, from the given set, the whole number is
\begin{array}{l}\require{cancel}
\{
0,\sqrt{4}
\}
.\end{array}
c) Integers include the numbers $\{...,-3,-2,-1,0, 1,2,3,...\}.$ Hence, from the given set, the integers are
\begin{array}{l}\require{cancel}
\{
-6,0,\sqrt{4}
\}
.\end{array}
d) Rational numbers are numbers that can be expressed as the ratio between two integers. Hence, from the given set, the rational numbers are
\begin{array}{l}\require{cancel}
\{
-6,0,0.\overline{7},\sqrt{4}
\}
.\end{array}
e) Irrational numbers are numbers that CANNOT be expressed as the ratio between two integers. Hence, from the given set, the irrational numbers are
\begin{array}{l}\require{cancel}
\{
-\pi,\sqrt{3}
\}
.\end{array}
f) Real numbers are all the numbers that can be represented in the real number line. Hence, from the given set, the real numbers are
\begin{array}{l}\require{cancel}
\{
-6,-\pi,0,0.\overline{7},\sqrt{3},\sqrt{4}
\}
.\end{array}