We know that y[n] = h[n] * x[n] where * denotes convolution. You have x[n] and y[n]. Let h[n] be denoted as [h0 h1 h2 etc.]. Use the defnition of the convolution sum to define y in terms of x[n] and h0. Then you can solve for h0. Repeat to define y in terms of x[n], h0, and h1. Solve for h1. Repeat until done. Recall that the convolution sum is defined as:
y(n) = symsum(x(k)*h(n-k),k,-inf,inf)
We can make a standard assumption that x[n] = y[n] = 0 for n < 0 absent any other information on the indexing of x and y. Therefore
y(n) = symsum(x(k)*h(n-k),k,0,inf)
But we also know that x[n] = 0 for n > 2. Therefore
y(n) = symsum(x(k)*h(n-k),k,0,2)
Now you can write a program to solve this equation for the unknown h[n]. In doing so, you'll have to figure out what values to assign to h[-1] and h[-2], and also account for the fact that matlab arrays use 1-based indexing but the development above assumes that the first value in the arrays x and y correspond to n = 0.
Once you get a result, you can check that it's correct using