Step 1 :Rearrange the expression to group the like terms together: \( (6 a^{4} c - 4 a^{4} c) + (8 a c^{2} - 10 a c^{2}) - 15 \)
Step 2 :Simplify each group of like terms: \( 2 a^{4} c - 2 a c^{2} - 15 \)
Step 3 :\(\boxed{2 a^{4} c - 2 a c^{2} - 15}\) is the simplified form of the given expression.