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To simplify the expression 12 - 4 ÷ 4/3 + 1, we first simplify the fraction 4/3 as a division problem.
4 ÷ 4/3 = 4 * 3/4 = 12/4 = 3
Now we can rewrite the expression as:
12 - 3 + 1
Next, we perform the addition and subtraction from left to right:
12 - 3 + 1 = 9 + 1 = 10
Therefore, the simplified expression is 10.