Answer
MR=6; MN=3; NT=3
Work Step by Step
Since TSR is a 30-60-90 degree triangle, RT is double of ST; this means that RT is 12. Since TSN and NSM are each 30 degrees, it follows that TSM is equilateral. Thus, NT and MN are equal. Since MS is a bisector, we know that MR is twice NT and MN. Thus, dividing the length of 12 up, we find:
$MR =6 \\ MN = 3 \\ NT =3 $