Please provide detailed explaination for each problem. Thank you.

Let $L_1=L(M_1)$ and $L_2=L(M_2),$ where $M_1=(\{1,2,3,4\},\{a,b\},{}_1,1,\{2,3\})$ and $M_2=$

$(\{1,2,3\},\{a,b\},{}_2,1,\{2\})$ as follows.

$($a$)$ Construct an NFA with $-$transitions for $L_1{L}_2.$

$($b$)$ Construct an NFA with $-$transitions for $(L_{1}U{L}_2{)}^{*}.$