a)
[tex]\it \dfrac{a}{b}=\dfrac{1}{2} \Rightarrow a=\dfrac{b}{2}\\ \\ \\ \dfrac{c}{b}=\dfrac{3}{2} \Rightarrow c=\dfrac{3b}{2}\\ \\ \\ a+c=\dfrac{b}{2}+\dfrac{3b}{2} \Rightarrow a+c=\dfrac{4b}{2} \Rightarrow a+c=2b\ \ \ \ (*)[/tex]
[tex]\it \dfrac{a+2b+c}{b} = \dfrac{a+c+2b}{b} \ \stackrel{(*)}{=}\ \dfrac{2b+2b}{b}=\dfrac{4b}{b} =4[/tex]
b)
[tex]\it a+c=6 \stackrel{(*)}{\Longrightarrow}\ 2b=6 \Rightarrow b=3.[/tex]
