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\[\frac{ 4 }{ 3 }x-\frac{ 15 }{ 6 } < 3x\]

multiply both sides by 6 first to remove annoying fractions

I'm sorry, how exactly do I multiply fractions?

for example
\[6\times \frac{4}{3}x=2\times 4x=8x\]the denominator is now gone

and of course
\[-\frac{15}{6}\times 6=-15\]

so the denominator gets canceled and the numerator becomes a whole number by itself?

long and the short of it is you should end up with
\[8x-15\leq 18x\]

yes

do I cancel the denominator out in the other fraction as well?

yes you want to get rid of both denominators 3 and 6