Economics Math: Optimal allocation of free time from Core Econ website. MRT = MRS

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CONTEXT:
I have the following equation for MRT=MRS (marginal rate of transformation = marginal rate of substitution): $\frac{αy}{24-t} = \frac{ay}{bt}$

I am asked to "multiply through" by $\frac{t}{y}$, which gives the following result: $\frac{αt}{24-t} = \frac{a}{b}$

The "multiplying through by $\frac{t}{y}$" is what seems to be confusing me.

QUESTION
Can anyone show me the individual steps that get from $\frac{αy}{24-t} = \frac{ay}{bt}$ to the result $\frac{αt}{24-t} = \frac{a}{b}$?