A student made twice as many mistakes as he got correct answers. If he attempted $48$ questions in total, how many questions did he get right?

Let the number of correct answers obtained by the student be $x$.
According to the problem statement, the number of mistakes (wrong answers) made by him is twice the number of correct answers:

$$\text{Number of mistakes}=2x$$

The total number of questions attempted by him is the sum of correct answers and mistakes, which is given as $48$:

$$\text{Correct Answers}+\text{Mistakes}=\text{Total Questions}$$

$$x+2x=48$$

$$3x=48$$

$$x=\frac{48}{3}=16$$

Therefore, the number of questions he got right is $16$.