Two ways to do it:

Without algebra, just basic math:

Retrace what happened:

He ended up with 744 apples.

Before that, he received a delivery that quadrupled his supply, so
before that delivery he had only 744÷4 = 186 apples.

Before the person bought 30 apples he had 186+30 = 216 apples

That's only 90% of what he had before he sold 10%, and 216÷90% = 216÷0.9 = 240 apples. 

That's only 3/4th of what he had before he discarded 1/4, and 

240÷(3/4) = 240×(4/3) = 320.

Answer: 320.

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Using algebra:

He started with N apples:

He had to discard 1/4 of them

So after that, he had N - (1/4)N = N - 0.25N = 0.75N

he sold 10% 

So after that, he had 0.75N - 0.10(.75N) = 0.675N

Someone bought 30 more apples.  

So after that he had 0.675N - 30

He received a delivery that quadrupled his remaining supply 

So after that he had 4(0.675N - 30)

and he ended up with 744 apples.

So the equation is

4(0.675N - 30) = 744

Divide both sides by 4

0.675N - 30 = 186

Add 30 to both sides:

     0.675N = 216 

Divide both sides by 0.675

         N = 320.

Edwin