What is the length of side TS?2 is the square root of 6 units6 is the square root of 6 units24 units8 units

we know that

 in the triangle TQS
applying the Pythagorean theorem
QS²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1

in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2

in the triangle QTR
TQ²=TR²+36-----------> equation 3


I substitute 1 and 2 in 3
18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units

the answer is
TS=6√6 units 
6 is the square root of 6 units