Explanation:

Let the marks of the students are $$X_1,X_2,X_3......X_{45}$$
It is given that the marks of the two student which entered incorrectly that is $$28$$ and $$64$$
Let$$X_1=28$$ and $$X_2=64$$
Average marks of student when wrongly entered $$={\displaystyle \frac{28+64+X_3+......+X_{45}}{45}}=66$$
$$28+64+X_3+......+X_{45}=66\times 45$$
$$X_3+......+X_{45}=66\times 45-28-64----------------------(i)$$
It is given that correct marks are $$82$$ and $$46$$
After entering correct marks, new average will be $$={\displaystyle \frac{82+46+X_3+......+X_{45}}{45}}--------------(ii)$$
From equation (i) and (ii)
$$={\displaystyle \frac{82+46+66\times 45-28-64}{45}}$$
$$={\displaystyle \frac{3006}{45}}=66.8$$