Given,
Teachers = 60%
Non_teachers = 40%

1) 200 people attended the workshop.
Teachers = 120
But no other info is given to deduce teachers of language arts
Insufficient

2) 72 of the teachers who attended the workshop were not teachers of language arts.
We only know the percentage, but not the number of people attended the workshop
Insufficient

From (1) and (2),
Total teachers = Art language + non art language
Art Language = total teachers - non art language
= 120 - 76
= 48
Sufficient
option C is correct

What % of people who attended the workshop were teachers of language art.?

Statement 1
200 people attended the workshop
If 200 people attend the workshop, then 120 were teachers
x of 120 = Language art teachers
$$require\ \%=\frac{x}{200}\cdot100\ $$
but we don't know the value of x, hence statement 1 is INSUFFICIENT.

Statement 2
72 of the teachers who attended the workshop were not teachers of language arts.
Let no of people in attendance = y
If y people attended the workshop, then
$$\left(60\%of\ y\right)-72\ were\ teachers\ of\ language\ arts.$$
$$0.6y-72\ were\ teachers\ of\ language\ arts$$
$$required\ \%=\frac{\left(0.6y-72\right)}{y}\cdot100$$
But we don't know the value of y,
Hence, statement 2 is INSUFFICIENT.

combining statement 1 and 2 together
From statement 1, we know that y = 200
$$hence\ \frac{\left(0.6y-72\right)}{y}\cdot100$$
$$hence\ \frac{\left(\left(0.6\cdot200\right)-72\right)}{200}\cdot100$$
$$hence\ \frac{\left(120-72\right)}{200}\cdot100$$
$$\frac{\left(48\right)}{200}\cdot100=24\%$$
Both statements together are SUFFICIENT.

$$Answer\ is\ Option\ C$$