Frequency Response of 1st Order circuit
a)
Your start equation is missing a factor 6, which is the value of the resistor.

The frequency response would then be:

$$
G(S)=\frac{Y(S)}{U(S)}=\frac{3.(S+2)}{2.S+1} 
$$
b)When the the frequency is zero the cap is an open circuit and the resulting gain should be 6, which is the value of the the resisor is parallel with the source.

When the frequency approaches infinity, the cap is a short circuit and the gain should be the parallel combination of the two resistor. That would be 12/8, you will reach the same value after calculating the limit with S-->infinity of the equation above.