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To solve the inequality \(3(b - 4) + 2b > 3\), first, simplify the left side:
\[
3b - 12 + 2b > 3
\]
\[
5b - 12 > 3
\]
Next, add 12 to both sides:
\[
5b > 15
\]
Now, divide by 5:
\[
b > 3
\]
So, the solution set consists of all values of \(b\) that are greater than 3.
In set notation, this can be expressed as:
\[
\{b: b > 3\}
\]
Thus, the correct answer from the provided options is:
\(\{b: b > 3\}\)