let

x = ounces of 12% acid solution

y = ounces of 6% acid solution

she needs to prepare 24 ounces of a 7% hydrochloric acid solution

x + y = 24

the 12% of x + the 6% of y = 24 ounces of a 7% hydrochloric acid solution

0.12x + 0.06y = 0.07*24

by solving the system of equations

x + y = 24

0.12x + 0.06y = 0.07*24

we find

x = 4 oz

y = 20 oz

click here to see the step by step solution of the system of equations

she needs 4 ounces of 12% acid and 20 ounces of 6% acid solution.