f(g(x)) means you put g(x) where x is in the definition of f(x). Doing that, we have
... f(g(x)) = f(5x²-1) = 3(5x²-1)² -(5x²-1) +2
From here, it is a matter of simplifying.
... = 3(25x⁴ -10x² +1) -5x² +1 +2 . . . . . multiply out the square: (a+b)² = a²+2ab+b²
... = 75x⁴-30x² -5x² +3 +1 +2 . . . . . . . eliminate parentheses. Collect terms next.
... f(g(x)) = 75x⁴ -35x² +6