Question 304646
Break up the number line into four regions.
({{{-infinity}}},{{{-3}}})
({{{-3}}},{{{0}}})
({{{0}}},{{{3}}})
({{{3}}},{{{infinity}}})
Then for each region pick a point (not the endpoints). 
Test the inequality.
If it solves it, that region is part of the solution. 
Then move on to the next region.
Region 1:
({{{-infinity}}},{{{-3}}})
Let {{{x=-4}}}
{{{2x(x+3)(x-3)<0}}}
{{{2(-4)(-4+3)(-4-3)<0}}}
{{{2(-4)(-1)(-7)<0}}}
{{{-56<0}}}
True, first region is part of the solution.
Move on.
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Region 2:
({{{-3}}},{{{0}}})
Let {{{x=-1}}}
{{{2x(x+3)(x-3)<0}}}
{{{2(-1)(-1+3)(-1-3)<0}}}
{{{2(-1)(2)(-4)<0}}}
{{{16<0}}}
False, second region is not part of the solution.
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Continue to the third and fourth regions to complete the solution. 
Re-post if you need more help.