Step 1 :Substitute $x=9$ into the expression $6+3(x-7)^{2}$
Step 2 :Calculate the value inside the parentheses: $9-7=2$
Step 3 :Square the result: $2^{2}=4$
Step 4 :Multiply by 3: $3*4=12$
Step 5 :Add 6: $6+12=18$
Step 6 :So, the final answer is \(\boxed{18}\)