One number is bigger than another by 406. if the bigger number is divided by the smaller one, you’ll get the quotient 3 and remainder 66. find the numbers.

Let's named numbers, first a and the second b.

a=b+406  ∧  a/b=3(66) this is not appropriate form of equation.
 
The next is better  a= 3b+66

Then we replace a in the first and get

b+406=3b+66 if we add (-66) to the both sides we get

b+406-66=3b then we add (-b) to the both sides and get

340=3b-b => 2b=340 => b=340/2 => b=170

when we replace this result at first equation we get

a= 170+406 = 576 => a=576

Good luck

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