Those Hardy-Weinberg equations are the general case, used for only two alleles. This question is basically answered here, for three alleles; you've got a situation of four alleles. That means you need to have:
(p+q+r+s)2=1
Where p, q, r, and s are the frequencies of your respective alleles. This expands out to the rather unwieldy:
p2+2pq+2pr+2ps+q2+2qr+2qs+r2+2rs+s2=1
Now it becomes a plug 'n chug assignment; simply assign the frequencies and calculate.
Assuming p is Adh-1, q is Adh-2, etc., p2=0.0121, 2pq=0.1848, and so on.
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