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For example, if we were just told that if we invest $400$ units now , and $250$ units 1 year from now, and are told it grows to $750$ units 2 years from now, and we want to find the effective annual interest rate.

But we are not told if it is simple or compound, can it still be done?

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From Wikipedia (emphasis by me):

The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.

Hence the initial investment of 400 units is worth $400\cdot q^2$ and the second investment $250\cdot q$ units (where $q=1+\frac{p}{100}$). So you are expectd to solve $$ 400 q^2+250q=750$$ and from that find $p$.

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    Thanks but wont we need to know if the accumulation is (1+it) or (1+i)^t ? – 2017-01-14
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    so we do or do not? – 2017-01-15
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    @PersonaA See the emphasis on "annual compound interest". – 2017-01-15