Assume that a black guinea pig crossed with an albino guinea pig produced 5 black offspring. when the albino was crossed with a second black guinea pig, 4 black and 3 albino offspring were produced. what genetic explanation would apply to these data?

As a matter of terminology, albino guinea pig actually refers to a white fur guinea pig, whose genotype is homozygous recessive (bb).

If it crossed with a black fur guinea pig and gave 5 black fur offsprings, there is a good chance that the black fur parent is homozygous dominant (BB).
The Punnett square would be as follows:

       B      B
b     Bb   Bb
b     Bb   Bb
So they are all heterozygous black fur offsprings.

However, it is not impossible that the black fur parent be heterozygous, namely

       B      b
b    Bb   bb
b    Bb   bb

Giving a 50% chance on each colour.  Thus it is possible (with probability 1/32) that all five offsprings are heterozygous black fur if one of the parents was heterozygous.

In the second case, a homozygous recessive and a homozygous dominant parent will never give a white offspring.  So it is sure that the black fur parent is heterozygous, with the following Punnett square:

       B      b
b     Bb   bb
b     Bb   bb

With a 50% probability for each of Bb (black fur) and bb (white fur).
the distribution 4,3 demonstrates this perfectly.