Step 1 :Substitute $x=-3$ into the function $f(x)=2x-7$, we get $f(-3)=2(-3)-7=-6-7=-13$
Step 2 :Substitute $x=3$ into the function $f(x)=2x-7$, we get $f(3)=2(3)-7=6-7=-1$
Step 3 :Substitute $x=-a$ into the function $f(x)=2x-7$, we get $f(-a)=2(-a)-7=-2a-7$
Step 4 :Substitute $x=a$ into the function $f(x)=2x-7$, we get $f(a)=2a-7$, then multiply by $-1$, we get $-f(a)=-2a+7$
Step 5 :Substitute $x=a+h$ into the function $f(x)=2x-7$, we get $f(a+h)=2(a+h)-7=2a+2h-7$