we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
In this problem
SR/SP=RT/TQ
substitute the given values
12/27=(x-4)/(x+6)
solve for x
12(x+6)=27(x-4)
12x+72=27x-108
27x-12x=72+108
15x=180
x=12
Find QT
QT=x+6
QT=12+6=18
therefore
the answer is
QT=18