Answer
The 6 values for $x_{i},y_{i}$ and for $0\leq x \leq1$ are shown in the table below
Work Step by Step
We are given $\frac{dy}{dx}=4-y$
so that $g(x,y)=4-y$
Since $x=0, y=0$
$g(x_{0},y_{0})=4$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=0+4\times0.2=0.8$
Now $x_{1}=0.1, y_{1}=0.8$
and $g(x_{1},y_{1})=3.2$
Then $y_{2}=0.8+3.2\times0.2=1.44$
$y_{3}=1.952$
$y_{4}=2.362$
$y_{5}=2.69$
$y_{6}=2.951$