Question 356808
{{{4x+y-4x=6-4x}}}
{{{y=6-4x}}}
{{{highlight(y=-4x+6)}}}<--- That's the equation of a straight line.
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Now graph the line, you could also use your intercepts.
{{{drawing(300,300,-8,8,-8,8,grid(1),circle(0,6,0.3),circle(3/2,0,0.3),graph(300,300,-8,8,-8,8,-4x+6))}}}
Choose a point not on the line. 
({{{0}}},{{{0}}}) is always a convenient choice.
Test the inequality.
{{{4x+y<=6}}} 

If the inequality is satisfied, shade the region that contains ({{{0}}},{{{0}}}).
Otherwise shade the other region.