Explain...?

Let's call the number that one is thinking of "x."

If I take "x" and I multiply "x" by 3, then I have "3x."

If I take "3x" and I add "4," then I have "3x+4."

If I have "3x+4" and I divide by 4, then I have $\frac{3x+4}{4}$.

If the original number is "x," then three less than "x" is x-3.

We know that $\frac{3x+4}{4}$ and $x-3$ are equivalent because of the keyword "is." 

Therefore, the final algabraic equation would be $\frac{3x+4}{4}=x-3$

Sure, you can:

Solve for x:

(3 x + 4)/4 = x - 3  cross multiply

3x + 4 = 4x - 12    move x to the LHS

3x - 4x = - 12 - 4

- x = - 16              Multiply both sides by -1

x = 16