Replace exponents by conversion to powers of 2 and expand:
2^24/2^(20x+16)=2^6/2^(10x).
Start simplifying exponents (e.g., divide through by 2^6):
2^18/2^(20x+16)=2^(-10x).
Continue to work with exponents:
2^(18-20x-16)=2^(-10x).
Simplify and equate exponents:
2-20x=-10x;
10x=2, x=0.2.
CHECK:
16^6*(1/4)^10=64/4=16
2^24/2^20=16 OK!