Which of the following points lie in the solution set?

By option verification,

i.e., substituting the options in given linear inequations and verifying

Given, $2x+3y>2$

$x-y<0$

$y\geq 0$

$x\leq 3$

substituting option A (i.e.,) $(x,y)=(1,1)$

$2x+3y>2\implies 2\times 1+3\times 1>2 \implies 5>2$ True

$x-y<0 \implies 1-1<0 \implies 0<0$ False

$y\geq 0 \implies 1\geq 0$ True

$x\leq 3 \implies 1\leq 3$ True

substituting option B (i.e.,) $(x,y)=(1,2)$

$2x+3y>2\implies 2\times 1+3\times 2>2 \implies 8>2$ True

$x-y<0 \implies 1-2<0 \implies -1<0$ True

$y\geq 0 \implies 2\geq 0$ True

$x\leq 3 \implies 1\leq 3$ True

substituting option C (i.e.,) $(x,y)=(2,1)$

$2x+3y>2\implies 2\times 2+3\times 1>2 \implies 7>2$ True

$x-y<0 \implies 2-1<0 \implies 1<0$ False

$y\geq 0 \implies 1\geq 0$ True

$x\leq 3 \implies 2\leq 3$ True

substituting option D (i.e.,) $(x,y)=(3,2)$

$2x+3y>2\implies 2\times 3+3\times 2>2 \implies 12>2$ True

$x-y<0 \implies 3-2<0 \implies 1<0$ False

$y\geq 0 \implies 2\geq 0$ True

$x\leq 3 \implies 3\leq 3$ True

Therefore option B satisfies the above linear inequalities.