Evaluating The Answer

$2x+3y=20$

$3y=20-2x$

$y=\frac{20-2x}{3}$

Now, $y$ is a whole number so, $20-2x$ must be divisible by $3$

For $x=1,4,7,10$ we have $y=6,4,2,0$

So, solutions are $(1,6),(4,4),(7,2),(10,0)$

There are $\boxed{ 4 }$ whole number solutions

We observe that x and y are whole numbers

Therefore x and y are either greater than or equal to 0 and cannot be fractions

If x=0,y=20/3 so not possible

If x=1,y=6 so possible

If x=2,y=16/3 so not possible

If x=3,y=14/3 so not possible

If x=4,y=4 so possible

If x=5,y=10/3 so not possible

If x=6,y=8/3 so not possible

If x=7,y=2 so possible

If x=8,y=4/3 so not possible

If x=9,y=2/3 so not possible

If x=10,y=0 so possible

Therefore the number of possible outcomes is 4