You can simply add the fractions in the most straightforward way, then reduce the result.
[tex]\frac{2}{3x^{2}+12x}+\frac{8}{2x} = \frac{(2(2x)+8(3x^{2}+12x)}{(3x^2+12x)(2x)}[/tex]
[tex]= \frac{24x^{2}+100x}{6x^{2}\times (x+4)} = \frac{2(6x+25)}{3x(x+4)}[/tex]
Or, you can reduce and factor the given fractions, find a common denominator, and use that.
[tex]\frac{2}{3x(x+4)}+\frac{4}{x} = \frac{2+4(3(x+4))}{3x(x+4)} =\frac{12x+50}{3x(x+4)}[/tex]
Either way, the expanded (some would say "simplified") result is
[tex]\frac{12x+50}{3x^{2}+12x}[/tex]
