jmc

The common denominator of $5$ and $4$ is $20$, so we multiply top and bottom of the first fraction by $4$ and multiply top and bottom of the second fraction by $5$. We get $$\frac{4(4+6a)}{4\cdot 5}-\frac{5(1+3a)}{4\cdot 5}=\frac{16+24a}{20}-\frac{5+15a}{20}.$$ We combine the fractions, being careful to put the numerator of the second fraction in parentheses (as we are subtracting the entire numerator), yielding $$\frac{16+24a-(5+15a)}{20}=\frac{16+24a-5-15a}{20}=\boxed{\frac{11+9a}{20}}.$$