Answer:[tex]10\sqrt{14})+8\sqrt{21})+30\sqrt{3}+36\sqrt{2})[/tex]Step-by-step explanation:The given product is:[tex](2\sqrt{7}+3\sqrt{6})(5\sqrt{2}+4\sqrt{3})[/tex]We expand using the distributive property to get;[tex](2\sqrt{7})(5\sqrt{2}+4\sqrt{3})+3\sqrt{6}(5\sqrt{2}+4\sqrt{3})[/tex]Simplify:[tex]=10\sqrt{14})+8\sqrt{21})+15\sqrt{12}+12\sqrt{18})[/tex][tex]=10\sqrt{14})+8\sqrt{21})+30\sqrt{3}+36\sqrt{2})[/tex]